Two-Timescale Hierarchical Reinforcement Learning for Resilient Operations
Authors: Young Hyun Cho, Franz Stoll, Will Wei Sun, Guang Lin, Stephan Biller
Organizations: Department of Statistics, Harvard University · Edwardson School of Industrial Engineering, Purdue University · Mitch Daniels School of Business, Purdue University · Department of Mathematics and School of Mechanical Engineering, Purdue University · Edwardson School of Industrial Engineering and Mitch Daniels School of Business, Purdue University · Dauch Center for the Management of Manufacturing Enterprises
Abstract
Unexpected shocks recur in global operations, requiring decision rules that adapt as market and operating conditions change. Many operational systems also have hierarchical structures in which long-term and short-term decisions pursue a shared objective. We study how hierarchical reinforcement learning can strengthen resilience by adapting these interdependent rules jointly. We develop a two-timescale hierarchical reinforcement learning framework that adapts long-term and short-term policies at their respective time scales. Because the policies are interdependent, we synchronize their updates and prove, to our knowledge, the first convergence guarantees for coupled two-timescale learning. Over T periods, our policies' average gap from an optimal policy pair is O(T−1/2), improving to O(logT/T) when poor decisions produce clearer profit losses. In a used-car case study, inventory replenishment is the long-term decision and customer-arrival pricing the short-term decision. Relative to the strongest partially adaptive benchmark, the framework increases mean profit by 9.2% under joint demand-supply shocks and by 11.8% under a prolonged shock scenario, while maintaining a more stable profit trajectory over time. Short-term adaptation addresses routine seasonality and one-sided disruptions by responding immediately to changing conditions. Under joint demand-supply shocks, however, it is insufficient alone; long-term adaptation is also needed to create favorable conditions for short-term decisions. Joint adaptation thus yields higher and more stable profits through disruption and recovery. Because many organizations already use hierarchical planning, the framework strengthens operational resilience without altering existing decision structures.
The combination of exponentially large action spaces, stochastic dynamics, and long-horizon decision-making under limited resources makes Sequential Stochastic Combinatorial Optimization (SSCO) particularly challenging for reinforcement learning. Hierarchical Reinforcement Learning (HRL) offers a natural decomposition, but it places the high-level policy in a Semi-Markov Decision Process (SMDP) where actions have variable durations, making it difficult to learn a world model that is suitable for planning. We introduce a model-based hierarchical framework for sequential stochastic combinatorial decision-making that directly addresses this issue. Our method combines a latent-space tree-search planner with an SMDP-aware world model for variable-duration decisions. A multi-timescale objective structures the latent dynamics so that transition magnitudes reflect the effective temporal scales of abstract actions, enabling efficient lookahead under adaptive temporal abstraction. We further learn a subgoal-conditioned budget policy jointly with the world model to support context-aware resource allocation. Across challenging SSCO benchmarks, our method outperforms strong baselines.
We present HBPI-UCRL, a model-based algorithm for hierarchical reinforcement learning (HRL) that learns high-level and low-level policies in parallel. HBPI-UCRL exploits the fact that a high-level transition corresponds to a multi-step transition at the low level. We introduce two conditions on the low-level dynamics that are sufficient to make parallel HRL learnable. When these conditions hold, we prove that HBPI-UCRL has a polynomial sample complexity in the problem parameters. In the sparse-reward, goal-directed setting, our sample complexity upper bound for HBPI-UCRL is strictly lower than that of its non-hierarchical counterpart, providing theoretical justification for the empirical success of HRL.
Anders Jonsson, Emilie Kaufmann, Gianmarco Tedeschi +1
Modern supply chain operations can require coordinating replenishment across thousands of heterogeneous items under correlated stochastic demand, heterogeneous lead times, and shared fixed ordering costs, yielding observation spaces exceeding 104 dimensions. At this scale, rolling-horizon stochastic mixed-integer linear programs (MILPs) become prohibitively slow, while standard reinforcement learning (RL) methods face increasingly challenging credit assignment in high-dimensional action spaces. We introduce OR-Transformer, a deep reinforcement learning framework for joint replenishment under stochastic demand, with an item-permutation-equivariant Transformer architecture and pathwise-gradient training through the inventory dynamics. Across problem sizes up to 1,024 inventory items, OR-Transformer increasingly outperforms learning-based and rolling-horizon MILP baselines as scale grows. It also reduces online decision-making time by over 4 million times relative to MILP solvers, enabling real-time, large-scale deep RL in supply chain operations.
Shuze Daniel Liu, David Simchi-Levi, Claire Chen +2