Speeding up Policy Simulation in Supply Chain RL

The document introduces the Picard Iteration algorithm, designed to accelerate policy simulation in supply chain optimization (SCO) problems by assigning policy evaluation tasks to independent processes and leveraging GPUs for batched evaluation, demonstrating practical speedups of 400x on large-scale SCO problems and proving convergence in a small number of iterations independent of the horizon.

Abstract

Simulating a single trajectory of a dynamical system under some state-dependent policy is a core bottleneck in policy optimization algorithms. The many inherently serial policy evaluations that must be performed in a single simulation constitute the bulk of this bottleneck. To wit, in applying policy optimization to supply chain optimization (SCO) problems, simulating a single month of a supply chain can take several hours. We present an iterative algorithm for policy simulation, which we dub Picard Iteration. This scheme carefully assigns policy evaluation tasks to independent processes. Within an iteration, a single process evaluates the policy only on its assigned tasks while assuming a certain 'cached' evaluation for other tasks; the cache is updated at the end of the iteration. Implemented on GPUs, this scheme admits batched evaluation of the policy on a single trajectory. We prove that the structure afforded by many SCO problems allows convergence in a small number of iterations, independent of the horizon. We demonstrate practical speedups of 400x on large-scale SCO problems even with a single GPU, and also demonstrate practical efficacy in other RL environments.

Method

The authors proposed an iterative approach to policy simulation called the Picard iteration, which is designed to address the time-consuming nature of simulating a fixed control policy in supply chain optimization (SCO) problems. The Picard iteration assigns policy evaluation tasks to independent processes and leverages GPUs for batched evaluation of the policy on a single trajectory. The algorithm is proven to converge in a small number of iterations independent of the horizon, demonstrating practical speedups of over 400x on large-scale SCO problems. Additionally, the authors theoretically establish that the Picard iteration achieves a non-trivial speedup over sequential computation in a large class of SCO problems. The methodology also involves the application of the Picard iteration to the Fulfillment Optimization (FO) problem, representative of a class of SCO problems targeted by reinforcement learning algorithms, and the experimental demonstration of the speedup achieved by the Picard iteration in policy optimization for FO instances using a policy gradient approach.

Main Finding

The authors made several key discoveries in their research. Firstly, they introduced the Picard Iteration algorithm, designed to accelerate policy simulation in supply chain optimization (SCO) problems, demonstrating practical speedups of over 400x on large-scale SCO problems. They also proved that the Picard iteration algorithm converges in at most QT + 1 iterations for the Fulfillment Optimization (FO) problem, under certain regularity conditions. Additionally, the authors explored the application of the Picard iteration to a class of SCO problems, theoretically establishing a non-trivial speedup over sequential computation. Furthermore, they discussed the potential value of the Picard framework in general environments, suggesting an end-to-end speedup of 13-40x in certain scenarios. Overall, the authors' discoveries centered around the effectiveness of the Picard Iteration algorithm in accelerating policy simulation and its potential impact on supply chain optimization and reinforcement learning environments.

Conclusion

The main conclusion of this paper introduces an algorithm called Picard iteration for accelerating strategy simulation in Supply Chain Optimization (SCO) problems, particularly in Fulfillment Optimization (FO) problems. The authors demonstrate that under certain assumptions, the Picard iteration algorithm can converge in no more than QT + 1 iterations. Additionally, the paper also shows the significant acceleration effect of Picard iteration in practical applications, such as achieving up to 400 times speedup using a single GPU. The paper also explores the potential applications of Picard iteration in other reinforcement learning environments and validates its effectiveness through experiments.

Keywords

Supply Chain Optimization, Policy Simulation, Picard Iteration, GPU Acceleration, Fulfillment Optimization, Reinforcement Learning, Parallel Discrete Event Simulation, Time Warp, Batch Evaluation, Policy Gradient, JAX, Consumer Surplus, Digital Economy, Product Variety, Online Booksellers, Sales Distribution Curve, Dual Mirror Descent, Online Allocation, Asynchronous Methods, Deep Reinforcement Learning, Environment Execution Engine, Sample Factory, Asynchronous Reinforcement Learning, Multi-Agent RL Environments, Bid-Price Controls, Network Revenue Management, Order Fulfillment, Prophet Inequality, Policy Parametrization, MLP, End-to-End Policy Optimization, Speedup, Conflicts, Heavy-Tailed Demand, Digital Twins, Dynamic Optimization, Intractable State-Spaces, Policy Evaluation, Iterative Algorithm, Convergence, Instance-Dependent Bound, JAXMARL, Proximal Policy Optimization, Differentiable Physics Engine, Rigid Body Simulation, CleanRL, Discovered Policy Optimisation.