From Ticks to Flows: Dynamics of Neural Reinforcement Learning in Continuous Environments
This work provides a novel theoretical foundation for understanding neural actor-critic algorithms in continuous RL, but the results are limited to single-hidden-layer networks and a toy task, making it incremental for the broader RL community.
This paper develops a theoretical framework for deep reinforcement learning in continuous environments, modeling it as a continuous-time stochastic process. For two-layer neural networks, they derive an equation describing the evolution of the state distribution under a vanishing learning rate, providing a nonparametric formulation for overparametrized actor-critic algorithms.
We present a novel theoretical framework for deep reinforcement learning (RL) in continuous environments by modeling the problem as a continuous-time stochastic process, drawing on insights from stochastic control. Building on previous work, we introduce a viable model of actor-critic algorithm that incorporates both exploration and stochastic transitions. For single-hidden-layer neural networks, we show that the state of the environment can be formulated as a two time scale process: the environment time and the gradient time. Within this formulation, we characterize how the time-dependent random variables that represent the environment's state and estimate of the cumulative discounted return evolve over gradient steps in the infinite width limit of two-layer networks. Using the theory of stochastic differential equations, we derive, for the first time in continuous RL, an equation describing the infinitesimal change in the state distribution at each gradient step, under a vanishingly small learning rate. Overall, our work provides a novel nonparametric formulation for studying overparametrized neural actor-critic algorithms. We empirically corroborate our theoretical result using a toy continuous control task.