Towards Painless Policy Optimization for Constrained MDPs
This addresses the problem of efficient and robust policy optimization for constrained reinforcement learning tasks, offering a method that reduces tuning overhead compared to existing approaches.
The paper tackles policy optimization in constrained Markov decision processes (CMDPs) by proposing the Coin Betting Politex (CBP) algorithm, which achieves reward sub-optimality and constraint violation bounds of O(1/((1-γ)^3√T) + ε_b√d/(1-γ)^2) and O(1/((1-γ)^2√T) + ε_b√d/(1-γ)), respectively, without requiring extensive hyperparameter tuning.
We study policy optimization in an infinite horizon, $γ$-discounted constrained Markov decision process (CMDP). Our objective is to return a policy that achieves large expected reward with a small constraint violation. We consider the online setting with linear function approximation and assume global access to the corresponding features. We propose a generic primal-dual framework that allows us to bound the reward sub-optimality and constraint violation for arbitrary algorithms in terms of their primal and dual regret on online linear optimization problems. We instantiate this framework to use coin-betting algorithms and propose the Coin Betting Politex (CBP) algorithm. Assuming that the action-value functions are $\varepsilon_b$-close to the span of the $d$-dimensional state-action features and no sampling errors, we prove that $T$ iterations of CBP result in an $O\left(\frac{1}{(1 - γ)^3 \sqrt{T}} + \frac{\varepsilon_b\sqrt{d}}{(1 - γ)^2} \right)$ reward sub-optimality and an $O\left(\frac{1}{(1 - γ)^2 \sqrt{T}} + \frac{\varepsilon_b \sqrt{d}}{1 - γ} \right)$ constraint violation. Importantly, unlike gradient descent-ascent and other recent methods, CBP does not require extensive hyperparameter tuning. Via experiments on synthetic and Cartpole environments, we demonstrate the effectiveness and robustness of CBP.