Contextual Bilevel Reinforcement Learning for Incentive Alignment
This work addresses incentive alignment in strategic decision-making for applications such as RLHF and mechanism design, though it appears incremental as it builds on existing bilevel optimization frameworks.
The paper tackles the problem of strategic decision-making where optimal policies depend on environmental configurations and exogenous events by introducing Contextual Bilevel Reinforcement Learning (CB-RL), a stochastic bilevel model that extends traditional bilevel optimization and is applied to fields like RLHF and tax design, with empirical demonstrations showing performance improvements in reward shaping and tax design scenarios.
The optimal policy in various real-world strategic decision-making problems depends both on the environmental configuration and exogenous events. For these settings, we introduce Contextual Bilevel Reinforcement Learning (CB-RL), a stochastic bilevel decision-making model, where the lower level consists of solving a contextual Markov Decision Process (CMDP). CB-RL can be viewed as a Stackelberg Game where the leader and a random context beyond the leader's control together decide the setup of many MDPs that potentially multiple followers best respond to. This framework extends beyond traditional bilevel optimization and finds relevance in diverse fields such as RLHF, tax design, reward shaping, contract theory and mechanism design. We propose a stochastic Hyper Policy Gradient Descent (HPGD) algorithm to solve CB-RL, and demonstrate its convergence. Notably, HPGD uses stochastic hypergradient estimates, based on observations of the followers' trajectories. Therefore, it allows followers to use any training procedure and the leader to be agnostic of the specific algorithm, which aligns with various real-world scenarios. We further consider the setting when the leader can influence the training of followers and propose an accelerated algorithm. We empirically demonstrate the performance of our algorithm for reward shaping and tax design.