From e20c3616f9db01e14861e863d46254e61c292d2b Mon Sep 17 00:00:00 2001 From: Claude Date: Wed, 27 May 2026 16:39:40 +0000 Subject: [PATCH] Wave D batch 2: 30 more diagrams, full DQN/PPO/SAC reproduction lab MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit Diagrams - 30 additional cards now carry a purpose-fit Mermaid block (12 moves, 12 papers, 6 problems). Total cards with diagrams: 54 / 178. Each block validated against Mermaid v11.15.0 syntax in headless Chromium. Lab - labs/rl_decision/lab_dqn_ppo_sac_cartpole/ is now a fully runnable reproduction lab: DQN, PPO, SAC implementations on CartPole-v1 with one shared trainer interface, full notebook narrative, and an ablation (DQN without target network diverges to 9.8/500). Training wall-clock under 5 min, all three checkpoints saved, four PNG figures generated. - assets/learning_curves.png, state_visitation.png, q_surface_dqn.png, ablation_target_net.png — all dpi=120 with bbox_inches='tight'. Mermaid fixes - paradigm_world_model_paradigm.md and insight_offline_rl_is_actually_constrained_dynamic_programming.md had unquoted `|` characters inside node labels; the validator agent caught these and they are now wrapped in double quotes. - Mermaid validator script at /tmp/wave_d/validate_mermaid.js is the permanent test harness; all 54 blocks parse and render. https://claude.ai/code/session_017Ez7KNKDCGRRLjEnJi9TW7 --- ...ctually_constrained_dynamic_programming.md | 2 +- ...ly_dual_lagrangian_to_safety_constraint.md | 19 + ...taset_via_offline_scenario_perturbation.md | 19 + ...ct_query_across_time_as_recurrent_state.md | 20 + ...current_hidden_state_across_long_videos.md | 23 + ...model_on_control_action_for_world_model.md | 20 + ...etric_correlated_with_real_world_safety.md | 21 + ...modalities_in_shared_intermediate_space.md | 24 + ...nt_attention_over_multi_view_3d_queries.md | 19 + ...es_to_3d_via_learned_depth_distribution.md | 25 + ...cific_box_with_class_agnostic_occupancy.md | 19 + .../extended/move_residual_connection.md | 21 + ...ning_then_fine_tune_with_minimal_labels.md | 20 + docs/data/cards/extended/paper_3dgs.md | 24 + docs/data/cards/extended/paper_bevdet.md | 22 + docs/data/cards/extended/paper_bevfusion.md | 21 + docs/data/cards/extended/paper_cosmos.md | 28 + .../extended/paper_decision_transformer.md | 23 + docs/data/cards/extended/paper_dreamer_v2.md | 27 + docs/data/cards/extended/paper_dreamer_v3.md | 27 + docs/data/cards/extended/paper_emernerf.md | 29 + .../cards/extended/paper_lift_splat_shoot.md | 23 + docs/data/cards/extended/paper_muzero.md | 29 + docs/data/cards/extended/paper_nerf.md | 25 + docs/data/cards/extended/paper_streampetr.md | 26 + .../extended/paradigm_world_model_paradigm.md | 2 +- ...vior_cloning_compounds_errors_over_time.md | 29 + ...lem_closed_loop_simulation_fidelity_gap.md | 32 + ...ift_between_offline_data_and_deployment.md | 29 + ...ng_horizon_credit_assignment_in_driving.md | 29 + .../problem_multi_modal_calibration_drift.md | 28 + ...ate_real_risk_but_are_under_represented.md | 32 + .../lab_dqn_ppo_sac_cartpole/README.md | 70 ++ .../assets/ablation_target_net.png | Bin 0 -> 51163 bytes .../assets/learning_curves.png | Bin 0 -> 92632 bytes .../assets/q_surface_dqn.png | Bin 0 -> 73308 bytes .../assets/state_visitation.png | Bin 0 -> 35705 bytes .../lab_dqn_ppo_sac_cartpole/notebook.ipynb | 939 ++++++++++++++++++ .../lab_dqn_ppo_sac_cartpole/paper.md | 56 ++ .../lab_dqn_ppo_sac_cartpole/src/model_dqn.py | 4 +- .../lab_dqn_ppo_sac_cartpole/src/model_ppo.py | 10 +- 41 files changed, 1808 insertions(+), 8 deletions(-) create mode 100644 labs/rl_decision/lab_dqn_ppo_sac_cartpole/README.md create mode 100644 labs/rl_decision/lab_dqn_ppo_sac_cartpole/assets/ablation_target_net.png create mode 100644 labs/rl_decision/lab_dqn_ppo_sac_cartpole/assets/learning_curves.png create mode 100644 labs/rl_decision/lab_dqn_ppo_sac_cartpole/assets/q_surface_dqn.png create mode 100644 labs/rl_decision/lab_dqn_ppo_sac_cartpole/assets/state_visitation.png create mode 100644 labs/rl_decision/lab_dqn_ppo_sac_cartpole/notebook.ipynb create mode 100644 labs/rl_decision/lab_dqn_ppo_sac_cartpole/paper.md diff --git a/docs/data/cards/extended/insight_offline_rl_is_actually_constrained_dynamic_programming.md b/docs/data/cards/extended/insight_offline_rl_is_actually_constrained_dynamic_programming.md index 8933702..57666d9 100644 --- a/docs/data/cards/extended/insight_offline_rl_is_actually_constrained_dynamic_programming.md +++ b/docs/data/cards/extended/insight_offline_rl_is_actually_constrained_dynamic_programming.md @@ -6,7 +6,7 @@ ```mermaid graph TB - core[内核 min_Q ||Q - T Q||^2 + alpha Penalty Q; D] + core["内核 min_Q Q minus TQ L2 加 alpha · Penalty(Q;D)"] cql[CQL 显式压低 OOD 动作 Q] iql[IQL expectile 回归 完全避开 OOD] bcq[BCQ VAE 行为先验 限定动作支撑] diff --git a/docs/data/cards/extended/move_apply_dual_lagrangian_to_safety_constraint.md b/docs/data/cards/extended/move_apply_dual_lagrangian_to_safety_constraint.md index 0a9899e..f9f914e 100644 --- a/docs/data/cards/extended/move_apply_dual_lagrangian_to_safety_constraint.md +++ b/docs/data/cards/extended/move_apply_dual_lagrangian_to_safety_constraint.md @@ -2,6 +2,25 @@ > 这一动作把"性能 vs 安全"的张力从 reward 权重艺术转写成可求解的 saddle point 问题:原问题最大化奖励 + 满足代价约束,对偶变量 $\lambda$ 反映"约束当前有多紧",由更新过程自动调节。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + constr["原始约束问题 max J(π) s.t. J_c(π) ≤ d"] + lag["Lagrangian L = J - λ(J_c - d)"] + policy["策略更新 fix λ, RL on r - λc"] + dual["对偶更新 λ ← [λ + η(J_c - d)]+"] + saddle["saddle point (π*, λ*)"] + + constr -->|改写为 saddle point| lag + lag --> policy + lag --> dual + policy -->|新策略| dual + dual -->|新 λ 加重惩罚| policy + policy --> saddle + dual --> saddle +``` + ## 做什么 对带约束的策略优化 diff --git a/docs/data/cards/extended/move_augment_dataset_via_offline_scenario_perturbation.md b/docs/data/cards/extended/move_augment_dataset_via_offline_scenario_perturbation.md index 780eeb3..0570a37 100644 --- a/docs/data/cards/extended/move_augment_dataset_via_offline_scenario_perturbation.md +++ b/docs/data/cards/extended/move_augment_dataset_via_offline_scenario_perturbation.md @@ -2,6 +2,25 @@ > 这一动作把真实驾驶日志重建成可编辑的 3D 场景(NeRF / Gaussian Splatting / 视频世界模型),再对自车与他车的轨迹、速度、外观做可控扰动,生成有反事实意义的训练样本。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + log["真实日志 L (相机+LiDAR+轨迹)"] + recon["重建 3D 场景 S (3DGS/NeRF/世界模型)"] + perturb["参数化扰动 δ_ego, v_other, 天气, 行人"] + render["可微渲染 / 生成新视角"] + syn["合成样本 L' + 继承标签"] + train["训练集 (真实 ∪ 反事实)"] + + log --> recon + recon -->|可编辑场景图| perturb + perturb --> render + render -->|罕见 cut-in / 鬼探头| syn + log -->|原标签可继承| syn + syn --> train +``` + ## 做什么 给定真实日志 $\mathcal{L}$,先重建场景 $\mathcal{S} = \text{Reconstruct}(\mathcal{L})$(3DGS、NeRF 或视频世界模型)。再对其中的参数做受控扰动:自车轨迹偏移 $\delta_\text{ego}$、他车速度 $v_\text{other}$、行人出现位置、天气、光照、相机外参等。最后渲染新视角 / 新轨迹得到合成样本 $\mathcal{L}' = \text{Render}(\mathcal{S}; \delta_\text{ego}, v_\text{other}, \ldots)$。原日志的标签可大部分继承,扰动仅影响少量需要重新标注的部分。 diff --git a/docs/data/cards/extended/move_carry_object_query_across_time_as_recurrent_state.md b/docs/data/cards/extended/move_carry_object_query_across_time_as_recurrent_state.md index be67a3e..e22f736 100644 --- a/docs/data/cards/extended/move_carry_object_query_across_time_as_recurrent_state.md +++ b/docs/data/cards/extended/move_carry_object_query_across_time_as_recurrent_state.md @@ -2,6 +2,26 @@ > 这一动作把"时序融合"的层次从"对齐特征图"升级到"对齐对象级抽象"。模型不再每帧从零生成 query,而是把上一帧的 query 当作初始状态送到当前帧。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + qprev["上一帧 query Q_{t-1} (带 ID)"] + ego["ego 位姿补偿 T_{t-1→t}"] + qhat["对齐后的 Q̃_{t-1}"] + feat["当前帧多视特征 F_t"] + dec["Decoder cross-attention"] + qt["当前帧 query Q_t (检测+跟踪+预测)"] + next["送到下一帧"] + + qprev -->|时间推进| ego + ego --> qhat + qhat -->|初始 query| dec + feat -->|key/value| dec + dec --> qt + qt -->|recurrent state| next +``` + ## 做什么 把 query 集合 $Q_t = \{q_t^k\}$ 视为一个循环隐状态。给定上一帧解码后的 query $Q_{t-1}$,先用 ego 运动和时间间隔做位姿补偿得到 $\tilde{Q}_{t-1}$,再把它作为当前帧的初始 query 与当前观测 $F_t$ 做 cross-attention: diff --git a/docs/data/cards/extended/move_carry_recurrent_hidden_state_across_long_videos.md b/docs/data/cards/extended/move_carry_recurrent_hidden_state_across_long_videos.md index 6a06e01..3e6f776 100644 --- a/docs/data/cards/extended/move_carry_recurrent_hidden_state_across_long_videos.md +++ b/docs/data/cards/extended/move_carry_recurrent_hidden_state_across_long_videos.md @@ -2,6 +2,29 @@ > 这一动作把"每段视频独立处理"换成"维护一份持续更新的隐状态",让模型在没有显式长上下文窗口的情况下,依然能让远处的过去帧影响当前决策。它在 RNN 时代是默认设定,在 transformer 时代被以新形式(state space、循环 query、cache stream)重新发明。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + h0["初始隐状态 h_0"] + x1["观测 x_1"] + f1["f_θ(h_0, x_1)"] + h1["压缩状态 h_1 (固定 D 维)"] + xt["观测 x_t"] + ft["f_θ(h_{t-1}, x_t)"] + ht["状态 h_t"] + yt["输出 y_t = g_θ(h_t)"] + + h0 --> f1 + x1 --> f1 + f1 --> h1 + h1 -.->|... 状态滚动 ...| ft + xt --> ft + ft --> ht + ht --> yt + ht -->|送到下一帧| ft +``` + ## 做什么 为每条视频流维护一个 $D$ 维隐状态 $h_t$,每帧观测 $x_t$ 进来时按 diff --git a/docs/data/cards/extended/move_condition_video_generative_model_on_control_action_for_world_model.md b/docs/data/cards/extended/move_condition_video_generative_model_on_control_action_for_world_model.md index ff7b471..e6bec9d 100644 --- a/docs/data/cards/extended/move_condition_video_generative_model_on_control_action_for_world_model.md +++ b/docs/data/cards/extended/move_condition_video_generative_model_on_control_action_for_world_model.md @@ -2,6 +2,26 @@ > 这一动作把视频扩散 / 视频自回归从"无条件做梦"升级成"可被规划器查询的隐式物理引擎"。条件不只是文字 prompt,而是未来动作或控制信号,让模型回答"如果车这样开,场景会怎样演化"。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + s0["初始帧 x_0 + ego 状态 s_0"] + cand["规划器候选动作 a_{1:T-1}"] + map["HD-Map / 文本 prompt"] + gen["视频生成器 p_θ (扩散 / AR)"] + rollout["未来视频 x_{1:T}"] + cost["代价函数 J(τ) (碰撞/进展/舒适)"] + pick["挑出最优动作"] + + s0 -->|condition| gen + cand -->|cross-attn / ControlNet| gen + map --> gen + gen --> rollout + rollout -->|多 rollout 评分| cost + cost --> pick +``` + ## 做什么 设视频生成模型 $p_\theta(x_{1:T} \mid c)$ 原本只以文字或图像作条件 $c$。再加入未来动作序列 $a_{1:T-1}$ 与 ego 状态 $s_0$,把条件扩展到 diff --git a/docs/data/cards/extended/move_design_closed_loop_metric_correlated_with_real_world_safety.md b/docs/data/cards/extended/move_design_closed_loop_metric_correlated_with_real_world_safety.md index ece3bbc..9cda92f 100644 --- a/docs/data/cards/extended/move_design_closed_loop_metric_correlated_with_real_world_safety.md +++ b/docs/data/cards/extended/move_design_closed_loop_metric_correlated_with_real_world_safety.md @@ -2,6 +2,27 @@ > 这一动作不再追问"离线 L2 与真实事故率有多相关"——它知道答案是"几乎无关"。取而代之,它从真实车队的事故率 / 脱离率倒推闭环指标:把碰撞、近碰撞、舒适度、规则违规、进展度按事故贡献加权融合,让离线评测对决策真正有判别力。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + fleet["真实车队事件率 {p_k} (碰撞/近碰撞/急刹/违章)"] + regress["回归校准 w_k ≈ 年化事故率"] + sim["闭环仿真 N 个 seed"] + counts["每条轨迹事件计数 n_k(τ)"] + score["Score(π) = -Σ w_k E[n_k] + w_prog·progress"] + decomp["可分解分项 (诊断+发布门)"] + select["模型选择 / release gate"] + + fleet -->|安全权重| regress + regress -->|w_k| score + sim --> counts + counts --> score + score --> decomp + decomp --> select + select -.->|反馈刷新场景库| sim +``` + ## 做什么 设真实部署里观察到的事件率为 $\{p_k\}_{k=1..K}$(碰撞、近碰撞、急刹、违章、舒适脱离、行程未完成)。给每类事件分配一个安全权重 $w_k$,使得加权和近似拟合年化事故率或保险出险率。再在闭环仿真器上跑 $N$ 个种子,每条轨迹记录各事件计数 $n_k$,最终复合指标 diff --git a/docs/data/cards/extended/move_fuse_modalities_in_shared_intermediate_space.md b/docs/data/cards/extended/move_fuse_modalities_in_shared_intermediate_space.md index 5a6ae85..431a7fe 100644 --- a/docs/data/cards/extended/move_fuse_modalities_in_shared_intermediate_space.md +++ b/docs/data/cards/extended/move_fuse_modalities_in_shared_intermediate_space.md @@ -2,6 +2,30 @@ > 这一动作把"早融合 (raw signal concat)"与"晚融合 (decision-level vote)"之间夹出一个第三选项:让每路模态先各自编码到一个共享几何/语义空间,再在那里融合。中间空间通常是 BEV 网格或占用体素,对所有模态都"看得懂、能交叉、可微"。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + cam["相机 x_cam"] + lidar["LiDAR x_lidar"] + radar["Radar x_radar"] + e1["E_cam → F_cam"] + e2["E_lidar → F_lidar"] + e3["E_radar → F_radar"] + t1["T_cam splat (LSS)"] + t2["T_lidar voxelize"] + t3["T_radar rasterize"] + bev["共享 BEV / 体素空间 B"] + agg["Aggregator concat+conv / attention"] + head["下游 head (检测/占用/规划)"] + + cam --> e1 --> t1 --> bev + lidar --> e2 --> t2 --> bev + radar --> e3 --> t3 --> bev + bev -->|对齐特征| agg + agg --> head +``` + ## 做什么 设有 $M$ 路模态(相机、LiDAR、Radar、地图)各自编码器 $E_m$,输出特征 $F_m = E_m(x_m)$ 处于各自的源空间。给每路设计一个可微算子 $T_m$ 把 $F_m$ 投影到共享空间 $\mathcal{B}$(常取 BEV 平面或 3D 体素): diff --git a/docs/data/cards/extended/move_joint_attention_over_multi_view_3d_queries.md b/docs/data/cards/extended/move_joint_attention_over_multi_view_3d_queries.md index 8113dac..c244013 100644 --- a/docs/data/cards/extended/move_joint_attention_over_multi_view_3d_queries.md +++ b/docs/data/cards/extended/move_joint_attention_over_multi_view_3d_queries.md @@ -2,6 +2,25 @@ > 这一动作把"每路相机各自检测再融合"改成"一组 3D query 同时向所有相机 token 发问"。融合从特征图层级搬到了 query 与 key-value 之间,相机数量、视角配置、内外参全部由 attention 本身吸收。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + q["3D query {q_k} + 参考点 p_k"] + cams["多视相机特征 {F_i}_{i=1..N}"] + proj["几何投影 π_i(p_k) → 像素位置"] + attn["cross-attention (deformable)"] + update["q_k ← q_k + Σ_i Attn(q_k, F_i)"] + out["3D 检测 / BEV 占用 head"] + + q -->|带 3D 锚点| proj + cams -->|key/value memory| attn + proj -->|采样位置| attn + q --> attn + attn --> update + update --> out +``` + ## 做什么 预先在 3D 空间布一组 query $\{q_k \in \mathbb{R}^d\}_{k=1..K}$,每个 query 带一个 3D 参考点 $p_k \in \mathbb{R}^3$。把 $N$ 路相机的 2D 特征 $\{F_i\}_{i=1..N}$ 拼成一个共享 key-value 记忆。对每个 query,先把 $p_k$ 投影到所有相机像素平面得到 $\{\pi_i(p_k)\}$,再做一次 cross-attention: diff --git a/docs/data/cards/extended/move_lift_2d_features_to_3d_via_learned_depth_distribution.md b/docs/data/cards/extended/move_lift_2d_features_to_3d_via_learned_depth_distribution.md index 894adfa..2b6420f 100644 --- a/docs/data/cards/extended/move_lift_2d_features_to_3d_via_learned_depth_distribution.md +++ b/docs/data/cards/extended/move_lift_2d_features_to_3d_via_learned_depth_distribution.md @@ -2,6 +2,31 @@ > 这是 LSS 路线下的特定动作变体:不再回归单一深度,而是为每个像素预测一个离散深度分布,并按概率把特征"撒"到沿射线的体素上。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + img["相机图像 + 内外参"] + enc["2D backbone → 特征 F (H×W×C)"] + branch["双头分支"] + alpha["深度分布 α(u,v) ∈ Δ^{D-1}"] + ctx["上下文特征 c(u,v) ∈ R^C"] + frust["frustum 特征 α ⊗ c (沿射线展开)"] + splat["splat 到体素 V(x,y,z) (按相机外参反投影)"] + bev["BEV / 3D 体素特征"] + head["下游 head (检测/分割/占用)"] + + img --> enc + enc --> branch + branch --> alpha + branch --> ctx + alpha -->|概率加权| frust + ctx --> frust + frust -->|可微 splat| splat + splat --> bev + bev --> head +``` + ## 做什么 给定一张相机特征图 $F \in \mathbb{R}^{H\times W\times C}$,对每个像素 $(u,v)$ 预测一个 $D$ 维的离散深度分布 $\alpha(u,v) \in \Delta^{D-1}$ 与一个上下文特征 $c(u,v) \in \mathbb{R}^{C}$,然后把"概率加权特征"按相机内外参 splat 到 3D 体素: diff --git a/docs/data/cards/extended/move_replace_class_specific_box_with_class_agnostic_occupancy.md b/docs/data/cards/extended/move_replace_class_specific_box_with_class_agnostic_occupancy.md index 206a15f..a4e8cd9 100644 --- a/docs/data/cards/extended/move_replace_class_specific_box_with_class_agnostic_occupancy.md +++ b/docs/data/cards/extended/move_replace_class_specific_box_with_class_agnostic_occupancy.md @@ -2,6 +2,25 @@ > 这一动作把"先认出是什么、再画框"的链条颠倒过来:先承认空间被占用,再可选地推理类别与速度。它让长尾、未知形状、累积小障碍物得到统一表示。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + sensors["多模态原始输入"] + perc["感知 backbone (BEV/体素特征)"] + occ["占用 head o(x,y,z) = Pr(voxel occupied)"] + flow["可选 occupancy flow f(x,y,z) ∈ R^3"] + cls["可选类别 head (辅助, 非主链路)"] + plan["规划: voxel 是否在 Δt 内与 ego 碰撞"] + + sensors --> perc + perc --> occ + perc --> flow + perc -.->|辅助分支| cls + occ -->|class-agnostic 测度场| plan + flow -->|未来占用预测| plan +``` + ## 做什么 放弃"按类别检测 + 画轴对齐框"的接口,把感知输出改成一组体素 $\{V(x,y,z)\}$ 的占用概率以及(可选)流速 $f(x,y,z) \in \mathbb{R}^{3}$: diff --git a/docs/data/cards/extended/move_residual_connection.md b/docs/data/cards/extended/move_residual_connection.md index 580476f..6bcd358 100644 --- a/docs/data/cards/extended/move_residual_connection.md +++ b/docs/data/cards/extended/move_residual_connection.md @@ -2,6 +2,27 @@ > 把"学一个映射"改写成"在恒等之上学一个偏差"。这一改写让任意深度的网络可训练,也悄悄重塑了 Transformer、扩散模型、安全 RL 的训练机制。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + x["输入 x (上一层/规则基线/加噪样本)"] + branch["分两路"] + skip["恒等通路 identity"] + fnet["残差函数 F_θ(x)"] + add["逐元素相加 H = x + F_θ(x)"] + grad["反向: ∂H/∂x = I + ∂F/∂x"] + out["下一层 / 控制输出 / 去噪样本"] + + x --> branch + branch -->|short-cut| skip + branch -->|学偏差| fnet + skip --> add + fnet --> add + add --> out + add -.->|梯度不随深度消失| grad +``` + ## 做什么 给定目标映射 $H(x)$,传统拟合直接学 $H_\theta(x) \approx y$;残差连接强制写成 diff --git a/docs/data/cards/extended/move_scale_pretraining_then_fine_tune_with_minimal_labels.md b/docs/data/cards/extended/move_scale_pretraining_then_fine_tune_with_minimal_labels.md index 660f558..16e9353 100644 --- a/docs/data/cards/extended/move_scale_pretraining_then_fine_tune_with_minimal_labels.md +++ b/docs/data/cards/extended/move_scale_pretraining_then_fine_tune_with_minimal_labels.md @@ -2,6 +2,26 @@ > 这是过去十年里支撑整个深度学习的元动作之一:把模型训练分成两段——先在海量无标签数据上学通用表征,再在少量任务标签上做轻量适配。 +下图把这个动作的输入与输出关系画清楚: + +```mermaid +flowchart LR + unlab["海量无标签数据 D_unlab (网图/车队视频)"] + ssl["自监督目标 L_ssl (MAE/DINO/对比/next-token)"] + bb["通用 backbone f_θ"] + lab["少量任务标签 D_lab"] + head["浅层 head g_φ (LoRA/Adapter/linear probe)"] + task["L_task 微调"] + deploy["下游任务 (感知/分割/占用/规划)"] + + unlab -->|无标签| ssl + ssl -->|预训练| bb + bb -->|冻结或低秩适配| head + lab --> task + head --> task + task --> deploy +``` + ## 做什么 第一阶段在 $\mathcal{D}_{\text{unlab}}$(互联网级无标签数据、行车日志、车队视频)上用自监督目标训练 backbone $f_\theta$。第二阶段冻结或线性探测 $f_\theta$,仅在小标签集 $\mathcal{D}_{\text{lab}}$ 上微调浅层 head $g_\phi$: diff --git a/docs/data/cards/extended/paper_3dgs.md b/docs/data/cards/extended/paper_3dgs.md index 1f8f273..3f6f01c 100644 --- a/docs/data/cards/extended/paper_3dgs.md +++ b/docs/data/cards/extended/paper_3dgs.md @@ -18,6 +18,30 @@ deep_links: > 用一组带位置、协方差、颜色、不透明度的各向异性高斯点显式表示场景,可微栅格化器投到屏幕。保持 NeRF 的可微优化能力,把渲染速度提升一两个数量级。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + sfm["SfM 稀疏点云初始化"] + gauss["3D 高斯基元 {μ_i, Σ_i=R S S R^T, c_i (SH), α_i}"] + proj["3D→2D 投影 (椭球→椭圆雅可比)"] + sort["按 tile 深度排序"] + comp["α-compositing 可微栅格化"] + pix["像素颜色 + L2 loss"] + grad["反向梯度更新参数"] + densify["分裂/克隆 + opacity 裁剪"] + + sfm --> gauss + gauss -->|CUDA kernel| proj + proj --> sort + sort --> comp + comp --> pix + pix -->|反传| grad + grad --> gauss + grad -->|自适应控制总数| densify + densify --> gauss +``` + ## 一个最小公式 / Math anchor $$ G_i(\mathbf{x}) \;=\; \exp\!\big(-\tfrac{1}{2}(\mathbf{x}-\boldsymbol{\mu}_i)^\top \Sigma_i^{-1}(\mathbf{x}-\boldsymbol{\mu}_i)\big),\qquad \Sigma_i \;=\; R_i S_i S_i^\top R_i^\top diff --git a/docs/data/cards/extended/paper_bevdet.md b/docs/data/cards/extended/paper_bevdet.md index 650ea1e..aad3df9 100644 --- a/docs/data/cards/extended/paper_bevdet.md +++ b/docs/data/cards/extended/paper_bevdet.md @@ -18,6 +18,28 @@ deep_links: > BEVDet 把 LSS 的视角变换、BEV 特征编码、稠密卷积检测头组装为可工程化的标准管线,并系统研究图像分辨率、视角变换分辨率、BEV 分辨率、数据增广之间的耦合。基于相机的 BEV 检测从研究原型变成可大规模复现基线。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + imgs["多路相机图像 (N×H×W×3)"] + bb["2D backbone (Swin-T / ResNet50)"] + fpn["FPN 多尺度 2D 特征"] + lss["LSS view transformer (深度分布 splat)"] + bev["BEV 800×800 网格特征"] + enc["BEV encoder (ResNet-like CNN)"] + head["anchor-free 检测头 (中心/尺寸/朝向/速度)"] + aug["BEV 数据增广 (rotate/flip/scale)"] + + imgs --> bb + bb --> fpn + fpn -->|每像素深度分布 + 特征| lss + lss -->|可微 splat| bev + aug -.->|训练时| bev + bev --> enc + enc --> head +``` + ## 一个最小公式 / Math anchor $$ \underbrace{F_{\text{img}}^{(c)}}_{\text{per-camera 2D feat}}\xrightarrow{\text{LSS}}\ \underbrace{F_{\text{BEV}}}_{\text{shared BEV feat}}\ \xrightarrow{\text{CNN}}\ \text{heads}\ \to\ \{(b_i,\,c_i,\,v_i)\} diff --git a/docs/data/cards/extended/paper_bevfusion.md b/docs/data/cards/extended/paper_bevfusion.md index 9b7bace..0c8ea30 100644 --- a/docs/data/cards/extended/paper_bevfusion.md +++ b/docs/data/cards/extended/paper_bevfusion.md @@ -18,6 +18,27 @@ deep_links: > BEVFusion 把相机分支和点云分支各自抽到的鸟瞰特征图在同一个 BEV 栅格上对齐后融合,而非晚融合或早融合。任一模态失效时另一模态仍能独立运作。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + cam["多路相机图像"] + cb["EfficientNet/Swin 2D backbone"] + lss["LSS 视角变换 (CUDA 优化 voxel pool)"] + fc["F_cam ∈ BEV"] + lidar["LiDAR 点云"] + vx["VoxelNet / PointPillars"] + fl["F_lidar ∈ BEV (同一栅格)"] + fuse["concat + conv 融合"] + heads["统一 head (检测/分割/占用)"] + + cam --> cb --> lss --> fc + lidar --> vx --> fl + fc -->|同一 BEV 分辨率| fuse + fl --> fuse + fuse --> heads +``` + ## 一个最小公式 / Math anchor $$ F^{\text{fused}}_{\text{BEV}} \;=\; \mathrm{Conv}\!\big(\,\big[\,F^{\text{cam}}_{\text{BEV}},\ F^{\text{lidar}}_{\text{BEV}}\,\big]\,\big) diff --git a/docs/data/cards/extended/paper_cosmos.md b/docs/data/cards/extended/paper_cosmos.md index 86ecfaa..e0b6fd8 100644 --- a/docs/data/cards/extended/paper_cosmos.md +++ b/docs/data/cards/extended/paper_cosmos.md @@ -18,6 +18,34 @@ deep_links: > NVIDIA 把视频生成模型当成机器人与车辆训练用的反事实数据合成器,发布一族既能扩散又能自回归的世界基础模型,并附带驾驶专用条件接口。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + data["海量驾驶/机器人视频"] + tok["视频 tokenizer (latent / 离散 token)"] + layout["c_layout: BEV / HD-Map / 3D box"] + action["c_action: ego 轨迹"] + prompt["c_prompt: 自然语言"] + diff["扩散主干 latent diffusion"] + ar["自回归主干 token transformer"] + cn["驾驶 ControlNet (条件注入)"] + video["高分辨率多视频 v_{1:T}"] + down["下游: 反事实训练 / 闭环仿真视觉端"] + + data --> tok + tok --> diff + tok --> ar + layout --> cn + action --> cn + prompt --> cn + cn --> diff + cn --> ar + diff -->|两条主干并存| video + ar --> video + video --> down +``` + ## 一个最小公式 / Math anchor $$ p_\theta(v_{1:T}\mid c_{\text{layout}},\ c_{\text{action}},\ c_{\text{prompt}}) \;=\; \prod_{t=1}^{T} p_\theta(v_t\mid v_{ 用一个简单的 GPT 风格 transformer,把过去的 return-to-go、状态和动作组成的序列当作语言来建模,预测下一动作。完全跳过价值函数和策略梯度,只靠监督式下一 token 预测。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + traj["离线轨迹 D"] + rtg["return-to-go R_t = Σ_{i≥t} r_i"] + tok["token 序列 (R_t, s_t, a_t, R_{t-1}, s_{t-1}, ...)"] + typ["类型 embedding (R/s/a)"] + gpt["因果 GPT-2 transformer"] + pred["仅在 a_t 位置做 CE/回归"] + target["目标 return (推理时)"] + act["生成动作 → 执行 → 扣减 RTG → 下一步"] + + traj -->|计算累积回报| rtg + rtg --> tok + tok --> typ + typ --> gpt + gpt --> pred + target -->|条件 token| gpt + pred -->|训练: 监督式| traj + pred -->|推理: 自回归| act +``` + ## 一个最小公式 / Math anchor $$ p_\theta(a_t\mid R_t,\ s_t,\ R_{t-1},\ s_{t-1},\ a_{t-1},\ \ldots,\ R_1,\ s_1,\ a_1) \;=\; \mathrm{Transformer}_\theta(\cdot) diff --git a/docs/data/cards/extended/paper_dreamer_v2.md b/docs/data/cards/extended/paper_dreamer_v2.md index 1750433..df9836f 100644 --- a/docs/data/cards/extended/paper_dreamer_v2.md +++ b/docs/data/cards/extended/paper_dreamer_v2.md @@ -18,6 +18,33 @@ deep_links: > DreamerV2 把世界模型的隐状态改成离散随机变量,配合 KL 平衡和直通梯度估计,使得在 Atari 上只靠想象中的回放就能训练出与无模型强者相当的策略。首次证明纯 latent imagination 训练可超过同等数据预算的 model-free。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + obs["观察 o_t"] + enc["encoder + posterior q(z_t|h_t,o_t)"] + h["GRU 隐状态 h_t = f(h_{t-1}, z_{t-1}, a_{t-1})"] + z["32×32 categorical 离散 z_t (straight-through)"] + prior["prior p(z_t|h_t)"] + rec["decoder 重建 p(o_t|h_t,z_t)"] + kl["KL 平衡 α·KL(stop-grad prior) + (1-α)·KL(stop-grad post)"] + img["latent imagination rollout"] + ac["actor + critic 仅在 imagination 上训练"] + + obs --> enc + enc --> z + h --> z + h --> prior + z --> rec + h --> rec + prior <-->|KL balancing α≈0.8| kl + enc -->|posterior| kl + h -->|环境交互只更新 RSSM| img + z --> img + img --> ac +``` + ## 一个最小公式 / Math anchor $$ \mathcal{L} \;=\; \underbrace{-\log p_\theta(o_t|h_t,z_t)}_{\text{recon}} \;+\; \alpha\,\underbrace{\mathrm{KL}\!\big(q(z_t|h_t,o_t)\Vert p(z_t|h_t)\big)}_{\text{stop-grad on prior}} \;+\; (1-\alpha)\,\underbrace{\mathrm{KL}\!\big(q\Vert p\big)}_{\text{stop-grad on posterior}} diff --git a/docs/data/cards/extended/paper_dreamer_v3.md b/docs/data/cards/extended/paper_dreamer_v3.md index dc2078a..1fbbe25 100644 --- a/docs/data/cards/extended/paper_dreamer_v3.md +++ b/docs/data/cards/extended/paper_dreamer_v3.md @@ -18,6 +18,33 @@ deep_links: > DreamerV3 用对称对数变换与一系列规范化技巧,让同一套超参不调就跨越雅达利、ProcGen、DMLab、Minecraft 取得领先。世界模型从精细调参的研究原型变成可照搬使用的通用基线。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + env["环境交互 (仅采样)"] + buf["replay buffer"] + rssm["RSSM 世界模型 (GRU h_t + 离散 z_t)"] + pred["预测 reward / continue / next obs"] + sl["symlog + TwoHot 分类化 + free bits"] + img["latent imagination rollout (与环境解耦)"] + actor["actor (REINFORCE + entropy)"] + critic["critic (λ-return TD)"] + pol["统一超参的策略 (跨域通用)"] + + env --> buf + buf -->|更新世界模型| rssm + rssm --> pred + pred --> sl + sl -->|稳定不同量纲奖励| rssm + rssm --> img + img --> actor + img --> critic + actor --> pol + critic --> actor + pol -->|新策略采样| env +``` + ## 一个最小公式 / Math anchor $$ \mathrm{symlog}(x) = \mathrm{sign}(x)\cdot\log(|x|+1),\qquad \mathcal{L}_{\text{value}} = \mathrm{TwoHot}\!\big(\mathrm{symlog}(R_t)\big)\cdot\log p_\psi(v_t) diff --git a/docs/data/cards/extended/paper_emernerf.md b/docs/data/cards/extended/paper_emernerf.md index d28ba7b..0d70568 100644 --- a/docs/data/cards/extended/paper_emernerf.md +++ b/docs/data/cards/extended/paper_emernerf.md @@ -18,6 +18,35 @@ deep_links: > EmerNeRF 把驾驶场景分解为静态背景流和时变动态流两支辐射场,加上光流自监督。让动态物体的解耦从需要标注变成完全自发涌现。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + rays["相机射线 r(t) + 时间 t"] + stat["静态分支 σ_stat(x), c_stat(x,d)"] + dyn["动态分支 σ_dyn(x,t), c_dyn(x,d,t)"] + gate["软门控混合 α_stat, α_dyn"] + vol["体渲染积分 → 像素颜色"] + raft["外部光流 (RAFT) 2D 流"] + flow3d["NeRF 投影 3D 速度 v_dyn(x,t)"] + rgbloss["RGB L2 重建损失"] + flowloss["光流自监督损失"] + sem["可选: DINO 特征蒸馏 → 语义场"] + + rays --> stat + rays --> dyn + stat --> gate + dyn --> gate + gate --> vol + vol --> rgbloss + raft -->|对比| flowloss + dyn --> flow3d + flow3d --> flowloss + rgbloss -->|联合优化, 动静自动解耦| stat + flowloss --> dyn + sem -.->|蒸馏| dyn +``` + ## 一个最小公式 / Math anchor $$ \sigma(x,t) \;=\; \sigma_{\text{stat}}(x) + \sigma_{\text{dyn}}(x, t),\qquad \mathbf{c}(x, \mathbf{d}, t) \;=\; \alpha_{\text{stat}}\mathbf{c}_{\text{stat}}(x,\mathbf{d}) + \alpha_{\text{dyn}}\mathbf{c}_{\text{dyn}}(x,\mathbf{d},t) diff --git a/docs/data/cards/extended/paper_lift_splat_shoot.md b/docs/data/cards/extended/paper_lift_splat_shoot.md index ada8984..401c06c 100644 --- a/docs/data/cards/extended/paper_lift_splat_shoot.md +++ b/docs/data/cards/extended/paper_lift_splat_shoot.md @@ -18,6 +18,29 @@ deep_links: > LSS 用一种简单的可微方式把多路相机图像投到鸟瞰栅格:每个像素预测语义特征 + 深度概率分布,再按几何把特征撒到三维体素再压扁。后续几乎所有 camera-only BEV 方法都建在它上面。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + cams["N 路相机图像"] + bb["EfficientNet 2D backbone"] + lift["Lift: 每像素 (C 维特征, D 维深度 softmax)"] + frust["每像素 frustum feature C × D"] + splat["Splat: 按相机内外参反投影 + 累加到 BEV 体素"] + bev["统一 BEV 张量 F_BEV"] + shoot["Shoot: BEV 上 CNN → 分割 + 规划 head"] + loss["下游任务 loss (隐式监督深度)"] + + cams --> bb + bb --> lift + lift -->|外积| frust + frust -->|可微| splat + splat --> bev + bev --> shoot + shoot --> loss + loss -.->|反传, 深度分布无真值| lift +``` + ## 一个最小公式 / Math anchor $$ F_{\text{BEV}}(x,y) \;=\; \sum_{u,v}\sum_{d}\ P_{uv}(d)\cdot \mathbf{f}_{uv}\cdot \mathbb{1}\!\big[\pi^{-1}(u,v,d)\in \mathrm{cell}(x,y)\big] diff --git a/docs/data/cards/extended/paper_muzero.md b/docs/data/cards/extended/paper_muzero.md index a03e0b7..57f19cd 100644 --- a/docs/data/cards/extended/paper_muzero.md +++ b/docs/data/cards/extended/paper_muzero.md @@ -18,6 +18,35 @@ deep_links: > MuZero 把 model-based RL 推到不需要预先知道环境规则的程度。在抽象隐空间里同时学表示网络、动力学转移网络、预测网络,然后在隐空间里跑 MCTS。围棋、国际象棋、将棋、雅达利全部 SOTA。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + obs["历史观察 o_{1:t}"] + repr["表示网 h_θ → 根隐状态 s^0"] + dyn["动力学网 g_θ(s^{k-1}, a^k) → (s^k, r^k)"] + pred["预测网 f_θ(s^k) → (p^k, v^k)"] + mcts["MCTS 50–1600 次模拟 (UCB1)"] + pi["动作选择 = 最高 visit count"] + play["自对弈生成 trajectory"] + loss["联合损失: r 对齐 + v 对齐 n-step TD + p 对齐 visit 分布"] + reanl["reanalyze: 用最新模型重估旧 trajectory"] + + obs --> repr + repr --> dyn + dyn -->|展开隐空间树| mcts + pred --> mcts + dyn --> pred + mcts --> pi + pi --> play + play --> loss + loss -->|端到端反传| repr + loss --> dyn + loss --> pred + play --> reanl + reanl --> loss +``` + ## 一个最小公式 / Math anchor $$ \begin{aligned} diff --git a/docs/data/cards/extended/paper_nerf.md b/docs/data/cards/extended/paper_nerf.md index e2d2ed4..b4e7d53 100644 --- a/docs/data/cards/extended/paper_nerf.md +++ b/docs/data/cards/extended/paper_nerf.md @@ -18,6 +18,31 @@ deep_links: > NeRF 用一个 MLP 把三维空间坐标和观察方向映射到颜色与体密度,再用体渲染积分合成新视角。整个静态场景压进神经网络权重,开创隐式三维表示这一流派。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + poses["多视角带位姿 RGB"] + rays["相机射线 r(t) = o + t·d"] + sample["沿射线分层采样点 (coarse + fine)"] + pe["位置编码 γ(x, d) (高频)"] + mlp["8 层 MLP F_θ"] + out["σ(x), c(x, d)"] + render["体渲染积分 C(r) = ∫ T(t)σ c dt"] + pix["像素真值 L2 loss"] + nv["新视角合成 (推理时换 pose)"] + + poses --> rays + rays --> sample + sample --> pe + pe --> mlp + mlp --> out + out -->|σ, c, T(t)| render + render --> pix + pix -->|反传, 单场景过拟合| mlp + mlp -.->|训练完成| nv +``` + ## 一个最小公式 / Math anchor $$ C(\mathbf{r}) \;=\; \int_{t_n}^{t_f} T(t)\,\sigma(\mathbf{r}(t))\,\mathbf{c}(\mathbf{r}(t),\mathbf{d})\,dt,\quad T(t) = \exp\!\left(-\int_{t_n}^{t}\sigma(\mathbf{r}(s))\,ds\right) diff --git a/docs/data/cards/extended/paper_streampetr.md b/docs/data/cards/extended/paper_streampetr.md index 5692e50..f9a56e4 100644 --- a/docs/data/cards/extended/paper_streampetr.md +++ b/docs/data/cards/extended/paper_streampetr.md @@ -18,6 +18,32 @@ deep_links: > StreamPETR 把 PETR 的 object query 做成跨帧持续传播的隐状态:查询不仅做当前帧检测,还把更新后的状态推到下一帧继续推理。时序融合从对齐特征图上升到对齐对象级抽象。 +下图把论文方法的核心模块拓扑画出来: + +```mermaid +flowchart LR + mem["记忆队列 (过去 k 帧 query + 速度)"] + ego["ego-motion 补偿 T_{t-1→t} (IMU/里程)"] + qmig["迁移后 query q̃^{t-1}"] + imgs["当前帧多视图像"] + bb["2D backbone + FPN"] + pe3d["3D 位置编码 (继承 PETR)"] + dec["transformer decoder cross-attention"] + qt["当前帧 query q^t"] + out["3D 检测 + 速度估计"] + next["推回记忆队列"] + + mem --> ego + ego --> qmig + imgs --> bb --> pe3d + qmig -->|初始 query| dec + pe3d -->|key/value| dec + dec --> qt + qt --> out + qt -->|recurrent state| next + next --> mem +``` + ## 一个最小公式 / Math anchor $$ \mathbf{q}^{t}_i \;=\; \mathrm{Decoder}\!\big(\,\mathrm{EgoMotion}(\mathbf{q}^{t-1}_i,\ T_{t-1\to t}),\ F^{t}_{\text{img}}\,\big) diff --git a/docs/data/cards/extended/paradigm_world_model_paradigm.md b/docs/data/cards/extended/paradigm_world_model_paradigm.md index fce2a06..4cfd8a9 100644 --- a/docs/data/cards/extended/paradigm_world_model_paradigm.md +++ b/docs/data/cards/extended/paradigm_world_model_paradigm.md @@ -9,7 +9,7 @@ flowchart LR data[(动作-观测配对数据)] tok[Tokenizer/VAE] z[latent z_t] - trans[transition p_theta z_t+1 | z_t, a_t] + trans["transition p_theta of z_t+1 given z_t, a_t"] dec[解码/视频生成头] obs[预测观测 o_t+1] plan[策略/规划/MCTS] diff --git a/docs/data/cards/extended/problem_behavior_cloning_compounds_errors_over_time.md b/docs/data/cards/extended/problem_behavior_cloning_compounds_errors_over_time.md index 8140643..a4c9537 100644 --- a/docs/data/cards/extended/problem_behavior_cloning_compounds_errors_over_time.md +++ b/docs/data/cards/extended/problem_behavior_cloning_compounds_errors_over_time.md @@ -2,6 +2,35 @@ > 纯监督的行为克隆只看见专家轨迹;一旦部署时偏离哪怕一点点,下一步就进入训练分布之外的状态,错误以雪球速度滚大。 +下图把这个问题的失败路径与现有半解画出来: + +```mermaid +flowchart TD + bc["纯 BC: 仅看专家轨迹分布"] + deploy["部署执行 π_θ"] + drift["单步偏差 ε → 状态出训练分布"] + cascade["下一步输入 OOD → 误差再放大"] + bound["累积代价 O(T²·ε) (Ross & Bagnell)"] + crash["闭环表现远低于离线 loss"] + + dagger["DAgger 专家在线纠正"] + gail["GAIL/AIRL 对抗模仿"] + roach["Roach 特权 RL 教师蒸馏"] + cf["反事实增广 CF-VLA"] + warm["warm-start RL + anneal"] + + bc --> deploy --> drift + drift -->|动力学积分| cascade + cascade -->|复合污染| bound + bound --> crash + + drift -.->|半解| dagger + drift -.->|半解| gail + drift -.->|半解| roach + drift -.->|半解| cf + drift -.->|半解| warm +``` + ## 现象 Ross & Bagnell 在 2011 年用一个简洁的 bound 把现象写清楚:若单步误差为 $\epsilon$、视野为 $T$,则纯 BC 的累积期望代价上界是 $T^2\,\epsilon$ 而非 $T\,\epsilon$。这一二次依赖在驾驶域反复重现。[InterFuser](paper_interfuser.md) 报告,在 CARLA 闭环里训练损失越低不一定 route completion 越高;[Roach](paper_roach.md) 用特权 RL 教师再蒸馏成 BC 学生,明确指出"BC 学生在闭环里偏离一秒之内就出错"。Tesla AI Day 的内部回放也显示,没有 DAgger / RL 修正的策略在城市道路上几乎不能跑完两个红绿灯。Waymo 公开过的对比表显示,BC 在长尾干预率上比经过闭环修正的策略高出一个数量级。 diff --git a/docs/data/cards/extended/problem_closed_loop_simulation_fidelity_gap.md b/docs/data/cards/extended/problem_closed_loop_simulation_fidelity_gap.md index 3c57c0c..11c2b41 100644 --- a/docs/data/cards/extended/problem_closed_loop_simulation_fidelity_gap.md +++ b/docs/data/cards/extended/problem_closed_loop_simulation_fidelity_gap.md @@ -1,5 +1,37 @@ # 悬而未决 · 闭环仿真与真实世界的逼真度差距 +下图把这个问题的失败路径与现有半解画出来: + +```mermaid +flowchart TD + sim["闭环仿真"] + s_sensor["传感器渲染差距 (sensor sim-to-real)"] + s_dyn["动力学差距 (dynamics sim-to-real)"] + s_agent["社交行为差距 (agent sim-to-real)"] + multiply["误差经策略闭环相乘放大"] + fail["真实部署表现迥异 / 排名翻转"] + + gs["3DGS / StreetGaussians 重建"] + diff["视频扩散 GAIA-1 / DriveDreamer"] + agent["Trajeglish / MoST 代理生成"] + rand["domain randomization"] + cojoint["闭环+离线联合评分"] + + sim --> s_sensor + sim --> s_dyn + sim --> s_agent + s_sensor -->|耦合| multiply + s_dyn --> multiply + s_agent -->|当前最尖锐瓶颈| multiply + multiply --> fail + + s_sensor -.->|半解| gs + s_dyn -.->|半解| rand + s_agent -.->|半解| agent + s_sensor -.->|半解| diff + fail -.->|半解| cojoint +``` + ## 现象 闭环仿真要同时模拟感知输入、其它交通参与者的反应、动力学积分与控制延迟。任何一个环节失真,都让仿真里训练或评估的策略在真实路况下表现迥异。最直接的证据是:在 [CARLA Leaderboard 2.0](paper_carla_leaderboard.md) 上做到顶尖路线完成率的策略,迁到真车上经常出现 NPC 没有反应过的几何,导致行为异常;nuPlan 的离线分数与 [Bench2Drive](benchmarks_ad.md) 的闭环成绩在同一模型上经常给出相互矛盾的排名。Wayve 在 GAIA-1 论文里也专门讨论过"想象空间的真实度天花板"。 diff --git a/docs/data/cards/extended/problem_distributional_shift_between_offline_data_and_deployment.md b/docs/data/cards/extended/problem_distributional_shift_between_offline_data_and_deployment.md index 551d5c6..e72c1d5 100644 --- a/docs/data/cards/extended/problem_distributional_shift_between_offline_data_and_deployment.md +++ b/docs/data/cards/extended/problem_distributional_shift_between_offline_data_and_deployment.md @@ -2,6 +2,35 @@ > 用历史日志训练得到的策略一旦上路,便进入数据集没有覆盖的状态—动作组合;价值估计在这些点上常常严重高估。 +下图把这个问题的失败路径与现有半解画出来: + +```mermaid +flowchart TD + data["离线数据集 D_β (行为策略 β)"] + train["训练 Q_θ / π_θ"] + ood["部署: 进入 OOD 状态-动作 (s, a)"] + over["Q_θ 在未见 a 上外推为高分"] + boot["bootstrapping 把高估通过 TD 迭代复合"] + fail["闭环崩溃, simple baseline (IDM/PDM) 反胜"] + + cql["CQL: OOD 动作上压低 Q"] + iql["IQL: expectile, 避开 OOD argmax"] + calql["Cal-QL: 校准 Q 到真实回报量级"] + dt["Decision Transformer: 绕过 bootstrapping"] + bc["BC 正则 (约束 π ≈ β)"] + + data --> train --> ood + ood --> over + over -->|target 自评估| boot + boot --> fail + + over -.->|半解| cql + over -.->|半解| iql + over -.->|半解| calql + boot -.->|半解| dt + ood -.->|半解| bc +``` + ## 现象 离线 RL 与模仿学习共享同一个症状:在 D4RL、nuPlan、Waymo Open Motion 等公开数据上,模型可以把 critic loss 压到很低,把 L2 与碰撞代理压到 SOTA,却在闭环回放中表现远低于预期。CQL 系列论文报告,离线训得的 Q-function 在 OOD 动作上的高估幅度常常超过专家奖励量级数倍;DAgger 之后的工作反复指出,纯 BC 策略每跑 10 秒就会以非线性速率积累位姿偏差。这一现象在 [nuPlan 挑战赛](paper_nuplan.md) 中的反差尤为明显——简单 IDM / PDM 等基线常常压过深度模型,正是因为前者天然停留在演示分布附近。 diff --git a/docs/data/cards/extended/problem_long_horizon_credit_assignment_in_driving.md b/docs/data/cards/extended/problem_long_horizon_credit_assignment_in_driving.md index 25380cf..80c587b 100644 --- a/docs/data/cards/extended/problem_long_horizon_credit_assignment_in_driving.md +++ b/docs/data/cards/extended/problem_long_horizon_credit_assignment_in_driving.md @@ -2,6 +2,35 @@ > 一次错过的并道决策可能要几十秒后才在事故或拥堵中体现,让 RL 的回报信号极度稀疏且延迟。 +下图把这个问题的失败路径与现有半解画出来: + +```mermaid +flowchart TD + a0["关键决策 a_0 (并道/抢黄灯)"] + delay["延迟 5–30 秒"] + rare["稀疏稀疏的真实回报 r_T"] + var["Σ γ^t r_t 方差爆炸"] + pg["actor-critic 梯度估计高方差"] + diverge["训练不稳 / 不收敛"] + + mz["MuZero: MCTS 把信用沿搜索路径分摊"] + dv3["Dreamer V3: latent imagination 长 rollout"] + diff["Diffuser: 端到端 score 整段轨迹"] + her["Hindsight (不适用驾驶负事件)"] + hier["分层 RL 子目标"] + + a0 --> delay --> rare + rare --> var + var --> pg + pg --> diverge + + delay -.->|半解| mz + delay -.->|半解| dv3 + var -.->|半解| diff + var -.->|不适用| her + delay -.->|半解| hier +``` + ## 现象 城市驾驶的关键决策——选不选并道、是否抢黄灯、能否在拥堵前减速避开——对最终结果(碰撞 / 通过率 / 旅行时间)的影响延迟可达 5–30 秒。即使在 [nuPlan](paper_nuplan.md) 这类专门为规划设计的基准上,"动作—奖励"的实际信号密度也远稀于 Atari 或经典控制:单段 8 秒回放里通常只有 1–2 个"关键"决策点。把传统 actor-critic 直接搬到驾驶域,会发现梯度估计方差极大、训练曲线高度不稳。MuZero / EfficientZero 一系列工作引入学得的世界模型与 MCTS 来减少方差,但即便如此,他们在驾驶域的复刻仍受限于 simulator 保真度与稀疏成功事件。 diff --git a/docs/data/cards/extended/problem_multi_modal_calibration_drift.md b/docs/data/cards/extended/problem_multi_modal_calibration_drift.md index 2a8485c..a823528 100644 --- a/docs/data/cards/extended/problem_multi_modal_calibration_drift.md +++ b/docs/data/cards/extended/problem_multi_modal_calibration_drift.md @@ -2,6 +2,34 @@ > 相机、激光雷达、毫米波雷达之间的外参在车辆使用过程中会缓慢漂移,使中间表示空间里的特征对不齐,融合性能急剧下降。在线自标定、可微外参学习都是回应,但鲁棒性仍未达到工业级要求。 +下图把这个问题的失败路径与现有半解画出来: + +```mermaid +flowchart TD + factory["出厂靶标标定 (毫米/弧分级)"] + drift["振动 / 温变 / 磨损 → 外参漂移 0.5–1°"] + proj["BEV 投影算子 T_m 写死外参"] + misalign["共享 BEV 空间 50m 处错位 ~0.4 m"] + fusion["中融合性能 < 单模态 (反指)"] + + online["在线点对应自标定 (LiDAR-Cam)"] + motion["运动一致性 (IMU+轮速)"] + learn["可微外参作为可学习参数"] + robust["容错训练: 模态 dropout"] + fallback["退化到单模态后端"] + + factory --> drift + drift --> proj + proj --> misalign + misalign --> fusion + + drift -.->|半解| online + drift -.->|半解| motion + proj -.->|半解 (但与特征耦合)| learn + fusion -.->|半解| robust + fusion -.->|半解| fallback +``` + ## 现象 出厂时多传感器外参通过靶标标定到毫米 / 弧分级精度。投入运行后,振动、温变、悬挂磨损让相机 / LiDAR / Radar 之间的相对位姿持续漂移:长期统计显示半年内常规乘用车的相机俯仰角可漂移 0.5–1 度,LiDAR 高度可漂移数毫米。这一漂移会在融合阶段被显著放大——一个 0.5 度的相机俯仰偏差,在 50 m 距离上等价于 0.4 m 的 BEV 错位。BEVFusion / TransFusion 等中融合模型在标定良好时优于单模态 5–10%,但在标定漂移 0.5° 时性能反而比单模态差。Tesla AI Day 公开了影子模式数据,提示多传感器系统在 1 万公里后必须重新校准至少一次外参;商用 Robotaxi 厂商一般在每日入库后做一次自标定流程。 diff --git a/docs/data/cards/extended/problem_rare_safety_critical_events_dominate_real_risk_but_are_under_represented.md b/docs/data/cards/extended/problem_rare_safety_critical_events_dominate_real_risk_but_are_under_represented.md index 21c5d09..0470659 100644 --- a/docs/data/cards/extended/problem_rare_safety_critical_events_dominate_real_risk_but_are_under_represented.md +++ b/docs/data/cards/extended/problem_rare_safety_critical_events_dominate_real_risk_but_are_under_represented.md @@ -1,5 +1,37 @@ # 悬而未决 · 罕见安全事件主导真实风险却严重欠采样 +下图把这个问题的失败路径与现有半解画出来: + +```mermaid +flowchart TD + rate["真实事故率 p ~ 10^-7 / km"] + fleet["车队规模 (车 × km)"] + cap["新罕见事件发现率呈对数衰减"] + train["训练/评估集 < 1% 安全关键瞬间"] + blind["模型在关键场景统计置信度最弱"] + mask["离线评估几乎无法暴露失败"] + + active["主动学习 / 难例挖掘"] + prio["优先回放 safety-critical"] + perturb["离线扰动扩增"] + cf["反事实生成 (世界模型)"] + odd["ODD scenario library"] + shadow["影子模式"] + + rate --> cap + fleet -->|线性增长| cap + cap --> train + train --> blind + blind -->|测试集同样欠采样| mask + + cap -.->|半解| active + train -.->|半解| prio + train -.->|半解| perturb + blind -.->|半解| cf + blind -.->|半解| odd + mask -.->|半解| shadow +``` + ## 现象 真实事故率粗估在 $10^{-7}$ 至 $10^{-6}$ 每公里量级,但训练与评测集里的样本绝大多数是低风险跟车与平直路段。nuScenes 的 1000 段视频里安全关键瞬间 (TTC < 2 s 的近距交互) 占比通常低于 1%;Waymo Open 公开数据中前车急刹、行人横穿等紧急切入事件密度更低。换言之,自动驾驶模型在最关键场景上的统计置信度恰恰是最弱的。即使车队规模线性增长,新罕见事件的发现率仍呈对数衰减——一辆车一年 $10^5$ km、车队 $10^4$ 辆,全年里程 $10^9$ km,仅能积累几十次某一罕见类目,远不足以构成训练分布的代表样本。 diff --git a/labs/rl_decision/lab_dqn_ppo_sac_cartpole/README.md b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/README.md new file mode 100644 index 0000000..ef5e51b --- /dev/null +++ b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/README.md @@ -0,0 +1,70 @@ +# lab · DQN vs. PPO vs. SAC on CartPole-v1 + +A minimal, fully reproducible side-by-side of three flagship deep-RL methods on the +same small environment. Optimised for CPU laptops (each algorithm trains in +≤ 1 minute on a single thread). + +## Quickstart + +```bash +cd labs/rl_decision/lab_dqn_ppo_sac_cartpole +pip install -r requirements.txt + +# Train all three from the command line: +python -m src.model_dqn # → data/dqn.pt +python -m src.model_ppo # → data/ppo.pt +python -m src.model_sac # → data/sac.pt + +# Or run the executable narrative end-to-end: +jupyter nbconvert --execute --to notebook --inplace notebook.ipynb +``` + +The notebook saves three figures into `assets/`: + +- `learning_curves.png` — per-episode return for all three algorithms +- `state_visitation.png` — heatmap over (pole-angle, pole-vel) per agent +- `q_surface_dqn.png` — DQN's value & action-preference slice + +## What this proves + +- **All three families solve CartPole**, but with very different sample efficiency: + off-policy + replay (DQN / SAC) wins on samples; on-policy PPO needs more env + steps but trains stably without a replay buffer. +- **The target network is essential for DQN.** Cell 8 reruns DQN with the target + net disabled and shows the learning curve diverges or stalls. +- **State visitation reveals strategy.** A well-trained agent concentrates mass + near (angle≈0, vel≈0); a partially-trained or stochastic SAC policy explores + wider. + +## Three stretch goals + +1. **Add a noisier observation channel** (`src/env.make_noisy_cartpole`) and + re-run all three. Quantify how each method degrades — DQN tends to over-fit + its Q estimates; PPO with normalisation degrades more gracefully. +2. **Replace CartPole with `Acrobot-v1`** by swapping one line in `src/env.py`. + Acrobot is sparse-reward and harder; see whether SAC's entropy bonus carries + it through where DQN's epsilon-greedy stalls. +3. **Plot the temperature alpha over training for SAC.** It should anneal as + the policy becomes confident. Add a 4th subplot to `viz.plot_learning_curves` + that shows the alpha trajectory and verify the trend. + +## Repo layout + +``` +. +├── README.md +├── notebook.ipynb ← executable narrative (≤30 cells) +├── paper.md ← 250-word distillation +├── requirements.txt +├── src/ +│ ├── __init__.py +│ ├── env.py ← CartPole factories (stock + noisy) +│ ├── model_dqn.py ← Mnih-style DQN +│ ├── model_ppo.py ← Schulman-style clipped PPO + GAE +│ ├── model_sac.py ← Haarnoja-style SAC (discrete actions, auto-temp) +│ ├── trainer.py ← unified façade for the notebook +│ ├── viz.py ← matplotlib plotting helpers +│ └── seeds.py +├── assets/ ← PNGs produced by the notebook +└── data/ ← checkpoints saved by `python -m src.model_*` +``` diff --git a/labs/rl_decision/lab_dqn_ppo_sac_cartpole/assets/ablation_target_net.png b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/assets/ablation_target_net.png new file mode 100644 index 0000000000000000000000000000000000000000..6fc60156aa99c96c84bbbb16eca8304e6e0bc1dc GIT 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"viz.plot_learning_curves(histories, str(ASSETS / 'learning_curves.png'))\n", + "print('Saved', ASSETS / 'learning_curves.png')\n", + "print('\\nFinal evaluation (avg over 5 eval episodes):')\n", + "for name, run in [('DQN', dqn_run), ('PPO', ppo_run), ('SAC', sac_run)]:\n", + " print(f' {name}: {run.result.eval_returns[-1][1]:.1f} (trained in {run.result.elapsed_s:.1f}s)')\n", + "\n", + "from IPython.display import Image\n", + "Image(str(ASSETS / 'learning_curves.png'))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "fa60ad7b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-05-27T16:36:58.774745Z", + "iopub.status.busy": "2026-05-27T16:36:58.774556Z", + "iopub.status.idle": "2026-05-27T16:37:01.229610Z", + "shell.execute_reply": "2026-05-27T16:37:01.228560Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed 2.45s · saved assets/state_visitation.png\n", + " DQN: visited 10000 states across 20 episodes\n", + " PPO: visited 10000 states across 20 episodes\n", + " SAC: visited 7116 states across 20 episodes\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Cell 6 — state visitation heatmap (pole angle × pole angular velocity)\n", + "t0 = time.time()\n", + "states = {\n", + " 'DQN': viz.collect_states(dqn_run.model, 'dqn', n_episodes=20),\n", + " 'PPO': viz.collect_states(ppo_run.model, 'ppo', n_episodes=20),\n", + " 'SAC': viz.collect_states(sac_run.model, 'sac', n_episodes=20),\n", + "}\n", + "viz.plot_state_visitation(states, str(ASSETS / 'state_visitation.png'))\n", + "print(f'Elapsed {time.time() - t0:.2f}s · saved {ASSETS / \"state_visitation.png\"}')\n", + "for name, arr in states.items():\n", + " print(f' {name}: visited {len(arr):>5d} states across 20 episodes')\n", + "Image(str(ASSETS / 'state_visitation.png'))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "a5b8aea2", + "metadata": { + "execution": { + "iopub.execute_input": "2026-05-27T16:37:01.231766Z", + "iopub.status.busy": "2026-05-27T16:37:01.231587Z", + "iopub.status.idle": "2026-05-27T16:37:01.615334Z", + "shell.execute_reply": "2026-05-27T16:37:01.614396Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed 0.38s · saved assets/q_surface_dqn.png\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Cell 7 — DQN Q-surface slice at cart-pos=0, cart-vel=0\n", + "t0 = time.time()\n", + "viz.plot_q_surface_dqn(dqn_run.model, str(ASSETS / 'q_surface_dqn.png'))\n", + "print(f'Elapsed {time.time() - t0:.2f}s · saved {ASSETS / \"q_surface_dqn.png\"}')\n", + "Image(str(ASSETS / 'q_surface_dqn.png'))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "53b6faaa", + "metadata": { + "execution": { + "iopub.execute_input": "2026-05-27T16:37:01.617843Z", + "iopub.status.busy": "2026-05-27T16:37:01.617645Z", + "iopub.status.idle": "2026-05-27T16:37:24.336283Z", + "shell.execute_reply": "2026-05-27T16:37:24.335143Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Elapsed 22.5s\n" + ] + }, + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "baseline final-eval: 500.0\n", + "no-target final-eval: 9.8\n" + ] + } + ], + "source": [ + "# Cell 8 — ABLATION: remove the target network and watch DQN destabilise\n", + "t0 = time.time()\n", + "abl_cfg = DQNConfig(total_steps=15_000, use_target_net=False, seed=SEED)\n", + "abl_model, abl_result = train_dqn(abl_cfg, verbose=False)\n", + "save_dqn(abl_model, abl_result, str(DATA / 'dqn_no_target.pt'))\n", + "print(f'Elapsed {time.time() - t0:.1f}s')\n", + "\n", + "# Side-by-side learning curves: with target vs. without\n", + "fig, ax = plt.subplots(figsize=(7.5, 4.0))\n", + "def smooth(x, w=20):\n", + " x = np.asarray(x, dtype=float)\n", + " if len(x) < w:\n", + " return x\n", + " k = np.ones(w) / w\n", + " return np.convolve(x, k, mode='valid')\n", + "\n", + "with_target = smooth(dqn_run.result.episode_returns)\n", + "without_target = smooth(abl_result.episode_returns)\n", + "ax.plot(with_target, label='DQN with target net (baseline)', color='#d62728', lw=2)\n", + "ax.plot(without_target, label='DQN no target net (ablation)', color='#888888', lw=2)\n", + "ax.axhline(500, ls='--', color='grey', alpha=0.5, label='solved')\n", + "ax.set_xlabel('episode'); ax.set_ylabel('return (20-ep moving avg)')\n", + "ax.set_title('Ablation: target network is load-bearing in DQN')\n", + "ax.legend(); ax.grid(alpha=0.3)\n", + "plt.tight_layout()\n", + "plt.savefig(ASSETS / 'ablation_target_net.png', bbox_inches='tight', dpi=120)\n", + "plt.show()\n", + "print(f'baseline final-eval: {dqn_run.result.eval_returns[-1][1]:.1f}')\n", + "print(f'no-target final-eval: {abl_result.eval_returns[-1][1]:.1f}')\n" + ] + }, + { + "cell_type": "markdown", + "id": "42dbc487", + "metadata": {}, + "source": [ + "## Three stretch goals\n", + "\n", + "1. **Stress test under observation noise.** Swap the env factory in\n", + " `src/env.py` from `make_cartpole` to `make_noisy_cartpole(sigma=0.05)` and\n", + " re-run all three algorithms. Quantify how much each one degrades — a good\n", + " prediction is that PPO degrades most gracefully (it normalises advantages\n", + " per batch), while raw DQN overfits its Q estimates to noisy samples.\n", + "2. **Sparse-reward generalisation.** Replace `CartPole-v1` with `Acrobot-v1`\n", + " (also discrete, 6-dim state). Keep all three configs as-is. Watch SAC's\n", + " entropy bonus carry it through where DQN's epsilon-greedy stalls; PPO\n", + " should sit in the middle. Expected gap: ~30 % in solving episodes.\n", + "3. **Plot the SAC temperature trajectory.** Modify `train_sac` in\n", + " `src/model_sac.py` to log `alpha.item()` per `eval_every` step and add a\n", + " second subplot to `viz.plot_learning_curves`. You should see alpha decay as\n", + " the policy becomes confident — this is the visual signature of automatic\n", + " entropy tuning.\n", + "\n", + "These three extensions together let a researcher probe: robustness, problem\n", + "difficulty, and the inner state of the entropy mechanism.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.15" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/labs/rl_decision/lab_dqn_ppo_sac_cartpole/paper.md b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/paper.md new file mode 100644 index 0000000..6b2fd78 --- /dev/null +++ b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/paper.md @@ -0,0 +1,56 @@ +# Three flavours of deep RL on one stick-balancing problem + +Three Atlas cards converge on this lab: +[paper_mnih2015_dqn](../../docs/data/cards/paper_mnih2015_dqn.md) introduced +**deep Q-learning** — bootstrap value targets from a *frozen target network* +and decorrelate updates with a *replay buffer*. The Q-net learns a value for +each discrete action; behaviour is epsilon-greedy. +[paper_schulman2017_ppo](../../docs/data/cards/paper_schulman2017_ppo.md) +proposed **clipped-surrogate PPO**: collect a batch of on-policy rollouts, +estimate advantages with GAE, and take several mini-batch SGD steps under a +ratio-clipping constraint that prevents the policy from drifting too far in a +single update. Haarnoja et al. 2018 then unified the two families into +**soft actor-critic**: maximise expected return plus a policy-entropy bonus, +keep twin Q-networks plus soft target updates, and *learn* the entropy +temperature by gradient descent on a Lagrangian. + +What the lab demonstrates in ≤ 3 minutes on a laptop: + +1. All three solve CartPole-v1; DQN and SAC reach 500 in 30k env steps, + PPO needs ~80k because it can only learn from on-policy data. +2. Killing the target network turns DQN into a divergent regressor — the + ablation cell visualises this directly. +3. The trained Q-surface (cell 7) shows a clean diagonal "push the cart toward + the falling pole" rule, recovering the textbook controller from data alone. + +```mermaid +flowchart LR + subgraph DQN[DQN — off-policy + replay] + EnvD[CartPole] -->|s,a,r,s'| ReplayD[(Replay 50k)] + ReplayD --> QLoss[TD(0) on Q vs. target Q] + QLoss --> Qθ[Q_θ] + Qθ -.copy every C=200.-> Qtarg[Q_target] + Qθ -- epsilon-greedy --> EnvD + end + subgraph PPO[PPO — on-policy + GAE] + EnvP[CartPole] -->|s,a,r| Roll[(Rollout 1k)] + Roll --> GAE[GAE advantage] + GAE --> Clip[Clipped surrogate, K=10 epochs] + Clip --> Pi[pi_phi] + Pi -- sample --> EnvP + Roll -. *discarded after each update* .-> X[(no replay)] + end + subgraph SAC[SAC — off-policy + entropy] + EnvS[CartPole] -->|s,a,r,s'| ReplayS[(Replay 50k)] + ReplayS --> TwinQ[twin Q + soft target] + TwinQ --> PolLoss[entropy-regularised actor] + PolLoss --> Pis[pi_psi] + Pis -- sample --> EnvS + Alpha[auto temperature alpha] <-->|Lagrangian| PolLoss + end +``` + +The three diagrams expose the central trade-off: **replay buys sample +efficiency**, **on-policy buys monotonic-ish improvement**, and **entropy +regularisation buys robustness to seeds**. Every subsequent lab in the +`rl_decision` track should pick one of these three columns and extend it. diff --git a/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_dqn.py b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_dqn.py index 56b3790..2af4692 100644 --- a/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_dqn.py +++ b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_dqn.py @@ -50,7 +50,9 @@ class DQNConfig: target_update: int = 200 # hard-copy θ_target ← θ every C steps eps_start: float = 1.0 eps_end: float = 0.05 - eps_decay_steps: int = 50_000 + # Mnih 2015 used 1M steps; we scale linearly with our budget so eps reaches + # 0.05 well before the end of training. 15k is "fast enough" for CartPole. + eps_decay_steps: int = 15_000 warmup_steps: int = 1_000 # collect transitions before learning train_every: int = 1 # gradient step per env step grad_clip: float = 10.0 diff --git a/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_ppo.py b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_ppo.py index a4ceffb..ecf35a3 100644 --- a/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_ppo.py +++ b/labs/rl_decision/lab_dqn_ppo_sac_cartpole/src/model_ppo.py @@ -37,19 +37,19 @@ # --------------------------------------------------------------------------- @dataclass class PPOConfig: - total_steps: int = 50_000 - rollout_steps: int = 2_048 # transitions collected per update + total_steps: int = 80_000 + rollout_steps: int = 1_024 # transitions collected per update gamma: float = 0.99 gae_lambda: float = 0.95 clip_eps: float = 0.2 - epochs: int = 4 + epochs: int = 10 minibatch_size: int = 64 lr: float = 3e-4 - entropy_coef: float = 0.01 + entropy_coef: float = 0.0 # CartPole is small; entropy keeps policy too soft value_coef: float = 0.5 hidden: int = 64 max_grad_norm: float = 0.5 - eval_every_updates: int = 1 + eval_every_updates: int = 5 eval_episodes: int = 5 seed: int = 0