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Modeling Boundedly Rational Agents with Latent Inference Budgets
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Introduces latent inference budget models (L-IBMs) that infer a latent per-agent computational budget controlling the runtime of anytime inference algorithms, and applies them to maze navigation, pragmatic language (RSA), and chess (MCTS).
Problem
Modeling populations of agents pursuing unknown goals under unknown computational constraints; standard Boltzmann models add homoscedastic noise to optimal decisions and cannot distinguish inference-budget differences that don't change action value.
Approach
Treat the inference budget as a latent variable that sets the runtime of an anytime inference algorithm (rather than a noise/temperature parameter), and jointly infer reward parameters and per-population budget distributions by marginalizing over budgets; tractable because anytime algorithms let all budget values be evaluated at roughly the cost of the largest one.
Key results
- In maze navigation, L-IBM recovers the true inference budgets nearly perfectly while the Boltzmann model shows no significant differences in inferred temperature across depth budgets.
- In Colors in Context, the inferred-budget L-IBM reaches 83.1% listener-target accuracy for player-skill stratification versus 81.8% for fixed depth-1 RSA and 80.4% for the literal listener (appendix table).
- In chess, inferred search budgets rise with player Elo, opponent Elo and time control, and L-IBM budgets consistently outperform the c_puct baseline by a small margin.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use inferred depth (L-IBM) instead of inferred temperature | RSA model · Colors in Context, player skill | accuracy: 82.3 -> 83.1 | Helped |
| use inferred depth (L-IBM) instead of inferred temperature | RSA model · Colors in Context, difficulty | accuracy: 82.7 -> 82.1 | Hurt |
| use fixed RSA depth 1 instead of literal depth 0 | RSA model · Colors in Context (speaker target) | accuracy: 80.4 -> 81.8 | Helped |
Surprising findings
- Boltzmann temperature showed no significant differences across true depth budgets in the maze task, showing it fails to capture inference-cost differences.
Limitations
- Requires the inference algorithm to be anytime so budgets can be marginalized efficiently.
- Chess and language experiments fit budget distributions per stratified group rather than per individual.
Experimental setup
Datasets: Colors in Context (reference games) lichess chess database (Jan/Feb 2019 releases) mazelib synthetic mazes
Benchmarks: Colors in Context lichess chess move prediction synthetic maze navigation
Metrics: exact-match action accuracy top-1 accuracy negative log-likelihood listener target accuracy
Baselines: Boltzmann model fixed-depth truncated search RSA with Boltzmann temperature imitation-learning policy beta_puct individual-difference MCTS model
Builds on: Boltzmann rationality models rational speech acts monte carlo tree search PUCT
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