Command-Space Counterfactual Explanations for Pareto-Conditioned Reinforcement Learning

Pareto Conditioned Networks learn multiple multi-objective reinforcement learning behaviours by conditioning a single policy on a desired return command. However, the local mapping from command and state to action remains opaque. We propose command-space counterfactual explanations for PCNs: given a fixed state, original command, and foil action, we search, in a black-box setting, for a minimally changed desired-return command under which the same trained policy would choose the foil. Our contributions are threefold. First, we formulate PCN explanations as return-command interventions, using a return-only PCN variant that avoids the added ambiguity of horizon-conditioning. Second, we adapt adversarial machine learning methods to reinforcement-learning explanations. Third, we introduce a boundary-seeded directional search that improves over purely local optimization in the command-action landscape, resulting in our proposed approach CF-ZOO. The resulting explanations are actionable and intuitively expressed in the user's own preferences: "If your trade-off had shifted slightly towards X, the agent would have chosen Y."

Bridging Spherical Black-Box Optimizers

When gradient information is unavailable, black-box optimization (BBO) methods provide a practical alternative. While Evolution Strategies (ES), Consensus-Based Optimization (CBO), Optimization via Integration (OVI), and related methods have each been studied independently, their connections remain underexplored. We unify these approaches within a common theoretical framework, revealing that they differ primarily in two design choices: fitness aggregation (controlling sharpness preference) and consensus scope (controlling modality). Leveraging these insights, we introduce hybrid optimizers that interpolate between existing methods. Our ES-OVI hybrid allows explicit control over the preference for flat minima, enabling a trade-off between performance and robustness in continuous control tasks. Our CBO-OVI hybrids combine the higher-dimensional efficiency of parametric methods with the multimodal capabilities of particle-based approaches, achieving competitive results on language model merging under limited evaluation budgets. We validate our methods on standard BBO benchmarks and higher-dimensional locomotion tasks, demonstrating that the hybrid methods can outperform their constituent algorithms.