Complexity-Driven Policy Optimization

Policy gradient methods often balance exploitation and exploration via entropy maximization. However, maximizing entropy pushes the policy towards a uniform random distribution, which represents an unstructured and sometimes inefficient exploration strategy. In this work, we propose replacing the entropy bonus with a more robust complexity bonus. In particular, we adopt a measure of complexity, defined as the product of Shannon entropy and disequilibrium, where the latter quantifies the distance from the uniform distribution. This regularizer encourages policies that balance stochasticity (high entropy) with structure (high disequilibrium), guiding agents toward regimes where useful, non-trivial behaviors can emerge. Such behaviors arise because the regularizer suppresses both extremes, e.g., maximal disorder and complete order, creating pressure for agents to discover structured yet adaptable strategies. Starting from Proximal Policy Optimization (PPO), we introduce Complexity-Driven Policy Optimization (CDPO), a new learning algorithm that replaces entropy with complexity. We show empirically across a range of discrete action space tasks that CDPO is more robust to the choice of the complexity coefficient than PPO is with the entropy coefficient, especially in environments requiring greater exploration.