Discovering Interpretable Multi-Parameter Control Policies for Evolutionary Algorithms Using Deep Reinforcement Learning
Authors: Tai Nguyen, Phong Le, Carola Doerr, Nguyen Dang
Organizations: University of St Andrews, St Andrews, United Kingdom · Sorbonne Universit´e, CNRS, LIP6, Paris, France
Abstract
While deep Reinforcement Learning (deep-RL) has been increasingly applied to parameter control in evolutionary algorithms, rigorous theoretical analysis of parameter control remains largely restricted to single-parameter settings, owing to the difficulty of deriving effective, interpretable multi-parameter policies amenable to formal study. We demonstrate how deep-RL can be leveraged to overcome this barrier, using the (1+(λ,λ))-genetic algorithm optimizing OneMax, one of the few problems where a super-constant speedup of dynamic control has been formally proven, as a representative case study. We first show that standard approaches struggle to converge in this multi-parameter setting, and introduce algorithm-agnostic enhancements targeting action-space decomposition, reward shifting, and long-horizon discounting. With these in place, we compare common deep-RL methods and find that Double Deep Q-Networks uniquely avoid the policy collapse observed in Proximal Policy Optimization, yielding trajectories suitable for downstream analysis. Crucially, we move beyond the ``black-box'' nature of neural networks by distilling the learned behaviors into a transparent, symbolic control policy. This resulting policy does not only offer interpretability for future theoretical analysis but also yields exceptional performance, consistently outperforming existing baselines across a wide range of problem sizes.
The temporal structure of reward composition in reinforcement learning (RL) is typically hand-designed and held fixed throughout training, leaving the progression of motivational priorities largely unexplored. In this work, we propose an evolutionary framework for discovering developmental reward schedules, in which three distinct biologically inspired motivational components -- agency, novelty, and reactivity -- are combined through time-varying weights that dynamically shift over the course of training. Evaluated on two sparse-reward MiniGrid tasks: DoorKey-6x6 and KeyCorridorS3R1, our framework compares the generalizability of four evolutionary algorithms: CMA-ES, xNES, DE, and L-SHADE against an extrinsically motivated baseline (our main comparison point), and three additional hand-designed methods. On DoorKey-6x6, all evolved methods outperform the non-evolved baselines, with L-SHADE achieving the best performance -- an approximate relative mean improvement of 11.4% over the extrinsic only baseline. On KeyCorridorS3R1, CMA-ES achieves the best overall performance, with the remaining evolved methods showing weaker and less reliable generalization capability compared to the extrinsic only baseline. Interestingly, the discovered schedules diverge from our defined developmental ordering, with novelty consistently emerging as the dominant early signal during training, across both tasks. Collectively, our results position evolutionary optimization as a promising approach for developmental reward schedule discovery in deep reinforcement learning, and suggest that what evolution finds to be optimal in computational settings may differ from what it finds to be optimal in biology. The code for this project can be found at: https://github.com/alannadels/Evolutionary_RL.git.
How does the amount of compute available to a reinforcement learning (RL) policy affect its learning? Can policies using a fixed amount of parameters, still benefit from additional compute? The standard RL framework does not provide a language to answer these questions formally. Empirically, deep RL policies are often parameterized as neural networks with static architectures, conflating the amount of compute and the number of parameters. In this paper, we formalize compute bounded policies and prove that policies which use more compute can solve problems and generalize to longer-horizon tasks that are outside the scope of policies with less compute. Building on prior work in algorithmic learning and model-free planning, we propose a minimal architecture that can use a variable amount of compute. Our experiments complement our theory. On a set 31 different tasks spanning online and offline RL, we show that (1) this architecture achieves stronger performance simply by using more compute, and (2) stronger generalization on longer-horizon test tasks compared to standard feedforward networks or deep residual network using up to 5 times more parameters.
Explainability remains a key issue in reinforcement learning (RL). Distilling an interpretable policy from an agent trained in a complex environment is particularly challenging when the action space is continuous. We introduce ORCAID, a novel method for extracting interpretable rule-based policies from RL agents operating in mixed continuous-discrete environments with continuous action spaces. Our main contribution is an efficient oblique decision tree training algorithm that partitions the state space by hyperplanes and fits local linear models. The key idea lies in a three-stage split search: efficient random initialization, local refinement, and backward elimination. Finally, adjacent leaves are merged to yield a concise set of interpretable rules describing a given deep RL policy. We evaluate ORCAID across multiple RL environments, demonstrating that the extracted rule-based policies maintain strong performance with a low number of parameters and can even be used to improve the performance of the original deep RL policy.
Ignacio D. Lopez-Miguel, Ezio Bartocci, Thomas Eiter +1