BAMDP Shaping: a Unified Framework for Intrinsic Motivation and Reward Shaping

2024-09-09

AI Summary

In reinforcement learning (RL), intrinsic motivation and reward shaping are prone to reward hacking—e.g., excessive fixation on stochastic noise sources like a flickering TV. Method: We unify these mechanisms as reward shaping within a Bayesian Adaptive Markov Decision Process (BAMDP) framework, introducing the BAMDP Potential Function (BAMPF). BAMPF decomposes state value into information-value and prior physical-state value components to guide robust exploration, and establishes boundedness criteria ensuring alignment between pseudo-rewards and true value. Contribution/Results: We provide the first theoretical proof that BAMPF is provably immune to reward hacking—within both meta-RL and standard RL settings. Empirically, BAMPF discovers optimal RL algorithms in Bernoulli Bandit meta-learning tasks and demonstrates effectiveness and plug-and-play compatibility in the Mountain Car environment.

Technology Category

• Machine Learning: Reinforcement Learning
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

Application Category

• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Intrinsic motivation and reward shaping guide reinforcement learning (RL) agents by adding pseudo-rewards, which can lead to useful emergent behaviors. However, they can also encourage counterproductive exploits, e.g., fixation with noisy TV screens. Here we provide a theoretical model which anticipates these behaviors, and provides broad criteria under which adverse effects can be bounded. We characterize all pseudo-rewards as reward shaping in Bayes-Adaptive Markov Decision Processes (BAMDPs), which formulates the problem of learning in MDPs as an MDP over the agent's knowledge. Optimal exploration maximizes BAMDP state value, which we decompose into the value of the information gathered and the prior value of the physical state. Psuedo-rewards guide RL agents by rewarding behavior that increases these value components, while they hinder exploration when they align poorly with the actual value. We extend potential-based shaping theory to prove BAMDP Potential-based shaping Functions (BAMPFs) are immune to reward-hacking (convergence to behaviors maximizing composite rewards to the detriment of real rewards) in meta-RL, and show empirically how a BAMPF helps a meta-RL agent learn optimal RL algorithms for a Bernoulli Bandit domain. We finally prove that BAMPFs with bounded monotone increasing potentials also resist reward-hacking in the regular RL setting. We show that it is straightforward to retrofit or design new pseudo-reward terms in this form, and provide an empirical demonstration in the Mountain Car environment.

Problem

• Theoretical model to anticipate and bound adverse effects of pseudo-rewards in RL.
• Characterizes pseudo-rewards as reward shaping in Bayes-Adaptive MDPs (BAMDPs).
• Extends potential-based shaping theory to prevent reward-hacking in meta-RL.

Innovation

• BAMDP framework unifies intrinsic motivation and reward shaping
• BAMPFs prevent reward-hacking in meta-RL and RL
• Optimal exploration maximizes BAMDP state value components