Claw Machine Experiment Data Modelling

Modelling claw machine experiment data using Optimal Bayesian decision-making agent. Confidence is given by the entropy of the Gibb's posterior.

• Each category is a univariate Gaussian N(μ, σ).
• On a trial the agent is offered two categories and must choose which one to sample from.
• An outcome is a success if the draw is below a fixed threshold (T), otherwise a failure.
• Rewards can differ between categories and are applied on success only.
• The agent maximises expected exponential utility

In main section of decision_maker.py:

- Adjust parameters of the ball distributions via "cats" dictionary
- Adjust rewards of the ball distributions via "rews" dictionary
- Provide pairs to evaluate via list of tuples called "pairs"
- When initialising the agent we need:
    - Threshold, T
    - Inverse temperature parameter, β
    - Decision-rule flag: if soft = False, then we do a MAP decision rule, otherwise soft sampling of the catgeory

• soft=True makes the agent sample from the posterior over actions.
  Set soft=False for the deterministic MAP choice. Adjust β parameter to adjust risk sensitivity of agent

• confidence is the negative entropy of that posterior (larger = more confident).