Risk-Sensitive Deep RL: Variance-Constrained Actor-Critic Provably Finds Globally Optimal Policy

TL;DR

This paper introduces a risk-sensitive deep reinforcement learning method that optimizes policies under variance constraints, providing theoretical guarantees of global optimality and demonstrating effectiveness on real datasets.

Contribution

It develops a novel actor-critic algorithm for variance-constrained policy optimization with provable convergence to a globally optimal policy.

Findings

The algorithm converges to a globally optimal policy at a sublinear rate.

The method effectively manages risk by constraining variance in long-term rewards.

Numerical studies validate theoretical results on real datasets.

Abstract

While deep reinforcement learning has achieved tremendous successes in various applications, most existing works only focus on maximizing the expected value of total return and thus ignore its inherent stochasticity. Such stochasticity is also known as the aleatoric uncertainty and is closely related to the notion of risk. In this work, we make the first attempt to study risk-sensitive deep reinforcement learning under the average reward setting with the variance risk criteria. In particular, we focus on a variance-constrained policy optimization problem where the goal is to find a policy that maximizes the expected value of the long-run average reward, subject to a constraint that the long-run variance of the average reward is upper bounded by a threshold. Utilizing Lagrangian and Fenchel dualities, we transform the original problem into an unconstrained saddle-point policy optimization problem, and propose an actor-critic algorithm that iteratively and efficiently updates the policy, the Lagrange multiplier, and the Fenchel dual variable. When both the value and policy functions are represented by multi-layer overparameterized neural networks, we prove that our actor-critic algorithm generates a sequence of policies that finds a globally optimal policy at a sublinear rate. Further, We provide numerical studies of the proposed method using two real datasets to back up the theoretical results.