Towards Enabling Learning for Time-Varying finite horizon Sequential Decision-Making Problems*

Abstract

Parameterized Sequential Decision Making (Para-SDM) framework models a wide array of network design applications spanning supply-chain, transportation, and sensor networks. These problems entail sequential multi-stage optimization characterized by states, control actions, and cost functions dependent on designable parameters. The challenge is to determine both the sequential decision policy and parameters simultaneously to minimize cumulative stagewise costs. Many Para-SDM problems are NP-hard and often necessitate time-varying policies. Existing algorithms tackling finite-horizon time-varying Para-SDM problems struggle with scalability when faced with a large number of states. Conversely, the sole algorithm addressing infinite-horizon Para-SDM assumes time (stage)-invariance, yielding stationary policies. However, this approach proves scalable for time-invariant problems by leveraging deep neural networks to learn optimal stage-invariant state-action value functions, enabling handling of large-scale scenarios. This article proposes a novel approach that reinterprets finite-horizon, time-varying Para-SDM problems as equivalent time-invariant problems through topography lifting. Our method achieves nearly identical results to the time-varying solution while exhibiting improved performance times in various simulations, notably in the small cell network problem. This fresh perspective on Para-SDM problems expands the scope of addressable issues and holds promise for future scalability through the integration of learning methods.