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
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.
Efficient resource allocation in multi-agent systems requires autonomous agents to coordinate their decisions while balancing system-wide objectives with individual costs. This becomes increasingly challenging over long time horizons, where decisions that improve the current allocation may compromise future resource allocation, while decentralized agents have limited observations of the overall system. Multi-agent reinforcement learning (MARL) can learn such long-term dependencies via local observations, but directly applying it to large-scale coordination leads to rapidly growing decision spaces and inefficient training. To this end, we propose Hierarchical Reinforcement and Collective Learning (HRCL), a hierarchical framework that uses MARL to guide, rather than replace, decentralized multi-agent coordination. At the high level, MARL learns strategies that restrict the alternatives considered during coordination and guide agents in balancing system-wide and individual objectives. At the low level, agents perform efficient decentralized coordination under this strategic guidance. This separation reduces the learning space and allows short-term coordination trade-offs to be evaluated according to their long-term effects. Experiments on a synthetic benchmark show that HRCL converges substantially faster than standalone MARL and reduces system-wide and individual costs by 35.53% and 27.05%, respectively. Evaluations on energy self-management and drone swarm sensing further show improved resource allocation, power-peak regulation, and sensing efficiency. These results show that learning strategic guidance for an existing coordination process can retain scalable decentralized coordination without letting short-term decisions compromise future resource allocation.
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