KIPPO: Koopman-Inspired Proximal Policy Optimization

2025-05-20

AI Summary

Reinforcement learning control in complex nonlinear dynamical environments suffers from high-variance gradient estimation and non-convex optimization, leading to unstable training. Method: This work proposes the first integration of Koopman operator theory into the Proximal Policy Optimization (PPO) framework. An auxiliary deep neural network is introduced to learn a linearized system dynamics model in a learned latent space, thereby decoupling dynamic modeling from policy optimization—without altering PPO’s original policy or value network architectures. The Koopman operator is approximated end-to-end via deep learning. Results: Extensive experiments on benchmark continuous-control tasks demonstrate consistent improvements: policy performance increases by 6–60%, and evaluation variance reduces by up to 91%. The method significantly enhances training stability and convergence robustness under nonlinear dynamics.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Learning with Manifolds
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and computational efficiency. These methods directly optimize policies through gradient-based updates. However, developing effective control policies for environments with complex and non-linear dynamics remains a challenge. High variance in gradient estimates and non-convex optimization landscapes often lead to unstable learning trajectories. Koopman Operator Theory has emerged as a powerful framework for studying non-linear systems through an infinite-dimensional linear operator that acts on a higher-dimensional space of measurement functions. In contrast with their non-linear counterparts, linear systems are simpler, more predictable, and easier to analyze. In this paper, we present Koopman-Inspired Proximal Policy Optimization (KIPPO), which learns an approximately linear latent-space representation of the underlying system's dynamics while retaining essential features for effective policy learning. This is achieved through a Koopman-approximation auxiliary network that can be added to the baseline policy optimization algorithms without altering the architecture of the core policy or value function. Extensive experimental results demonstrate consistent improvements over the PPO baseline with 6-60% increased performance while reducing variability by up to 91% when evaluated on various continuous control tasks.

Problem

• Addresses complex non-linear dynamics in RL control policies
• Reduces high variance in gradient estimates for stability
• Improves PPO performance via Koopman linear latent-space representation

Innovation

• Koopman-Inspired latent-space linearization for RL
• Auxiliary network enhances PPO without architecture changes
• Reduces gradient variance and improves learning stability