Faster Reinforcement Learning by Freezing Slow States (2301.00922v2)

Abstract: We study infinite horizon Markov decision processes (MDPs) with "fast-slow" structure, where some state variables evolve rapidly ("fast states") while others change more gradually ("slow states"). Such structure is common in real-world problems where sequential decisions need to be made at high frequencies over long horizons, where slowly evolving information also influences optimal decisions. Examples include inventory control under slowly changing demand, or dynamic pricing with gradually shifting consumer behavior. Modeling the problem at the natural decision frequency leads to MDPs with discount factors close to one, making them computationally challenging. We propose a novel approximation strategy that "freezes" slow states during a phase of lower-level planning, solving finite-horizon MDPs conditioned on a fixed slow state, and then applying value iteration to an auxiliary upper-level MDP that evolves on a slower timescale. Freezing states for short periods of time leads to easier-to-solve lower-level problems, while a slower upper-level timescale allows for a more favorable discount factor. On the theoretical side, we analyze the regret incurred by our frozen-state approach, which leads to simple insights on how to trade off computational budget versus regret. Empirically, we demonstrate that frozen-state methods produce high-quality policies with significantly less computation, and we show that simply omitting slow states is often a poor heuristic.