TMLR Journal 2026 Journal Article
Natural Policy Gradient for Average Reward Non-Stationary Reinforcement Learning
- Neharika Jali
- Eshika Pathak
- Pranay Sharma
- Guannan Qu
- Gauri Joshi
We consider the problem of non-stationary reinforcement learning (RL) in the infinite-horizon average-reward setting. We model it by a Markov Decision Process with time-varying rewards and transition probabilities, with a variation budget of $\Delta_T$. Existing non-stationary RL algorithms focus on model-based and model-free value-based methods. Policy-based methods despite their flexibility in practice are not theoretically well understood in non-stationary RL. We propose and analyze the first model-free policy-based algorithm, Non-Stationary Natural Actor-Critic, NS-NAC, a policy gradient method with a restart based exploration for change and a novel interpretation of learning rates as adapting factors. Further, we present a bandit-over-RL based parameter-free algorithm, BORL-NS-NAC, that does not require prior knowledge of the variation budget $\Delta_T$. We present a dynamic regret of $\mathcal{\tilde{O}} (|\mathcal{S}|^{1/2}|\mathcal{A}|^{1/2}\Delta_T^{1/6}T^{5/6})$ for both algorithms under standard assumptions, where $T$ is the time horizon, and $|\mathcal{S}|$, $|\mathcal{A}|$ are the sizes of the state and action spaces. The regret analysis leverages a novel adaptation of the Lyapunov function analysis of NAC to dynamic environments and characterizes the effects of simultaneous updates in policy, value function estimate and changes in the environment.