Trusted Approximate Policy Iteration with Bisimulation Metrics

• URL: http://arxiv.org/abs/2202.02881v1
• Date: Sun, 6 Feb 2022 22:41:56 GMT
• Title: Trusted Approximate Policy Iteration with Bisimulation Metrics
• Authors: Mete Kemertas, Allan Jepson
• Abstract summary: Bisimulation metrics define a distance measure between states of a Markov decision process (MDP) based on a comparison of reward sequences. In this work we first prove that bisimulation metrics can be defined via any $p$-Wasserstein metric for $pgeq 1$. We then describe an approximate policy iteration (API) procedure that uses $epsilon$-aggregation with $pi$-bisimulation and prove performance bounds for continuous state spaces.
• Score: 1.6498361958317633
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Bisimulation metrics define a distance measure between states of a Markov decision process (MDP) based on a comparison of reward sequences. Due to this property they provide theoretical guarantees in value function approximation. In this work we first prove that bisimulation metrics can be defined via any $p$-Wasserstein metric for $p\geq 1$. Then we describe an approximate policy iteration (API) procedure that uses $\epsilon$-aggregation with $\pi$-bisimulation and prove performance bounds for continuous state spaces. We bound the difference between $\pi$-bisimulation metrics in terms of the change in the policies themselves. Based on these theoretical results, we design an API($\alpha$) procedure that employs conservative policy updates and enjoys better performance bounds than the naive API approach. In addition, we propose a novel trust region approach which circumvents the requirement to explicitly solve a constrained optimization problem. Finally, we provide experimental evidence of improved stability compared to non-conservative alternatives in simulated continuous control.

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