Hybrid TD3: Overestimation Bias Analysis and Stable Policy Optimization for Hybrid Action Space

We study reinforcement learning in hybrid discrete-continuous action spaces, such as settings where the discrete component selects a regime (or index) and the continuous component optimizes within it -- a structure common in robotics, control, and operations problems. Standard model-free policy gradient methods rely on score-function (SF) estimators and suffer from severe credit-assignment issues in high-dimensional settings, leading to poor gradient quality. On the other hand, differentiable simulation largely sidesteps these issues by backpropagating through a simulator, but the presence of discrete actions or non-smooth dynamics yields biased or uninformative gradients. To address this, we propose Hybrid Policy Optimization (HPO), which backpropagates through the simulator wherever smoothness permits, using a mixed gradient estimator that combines pathwise and SF gradients while maintaining unbiasedness. We also show how problems with action discontinuities can be reformulated in hybrid form, further broadening its applicability. Empirically, HPO substantially outperforms PPO on inventory control and switched linear-quadratic regulator problems, with performance gaps increasing as the continuous action dimension grows. Finally, we characterize the structure of the mixed gradient, showing that its cross term -- which captures how continuous actions influence future discrete decisions -- becomes negligible near a discrete best response, thereby enabling approximate decentralized updates of the continuous and discrete components and reducing variance near optimality. All resources are available at github.com/MatiasAlvo/hybrid-rl.

Many real-world control problems involve hybrid discrete-continuous action spaces. For example, steering and signaling in autonomous driving, and aiming and firing in robotics or video-games. Despite real-world hybrid factorization and reinforcement learning framework support for complex action spaces (e.g., Gymnasium, PettingZoo, TorchRL, SeedRL, Mujoco, etc), the default environments within those frameworks often implement uniform action space configurations (LunarLander, Walker2D, Cheetah, SMAC, SUMO, Ant, Atari). Landmark hybrid-action benchmarks (RoboCup 2D HFO, SC2LE, Platform, CARLA, etc) are mostly heavyweight or archival implementations originating from papers which test one or a small number of competing factorization methods on one kind of control. This article provides a cross-sectional study of factorization methods [independent networks, shared encoder, VDN, QPLEX, Joint, Auto-Regressive] on each of three families of algorithms [PPO, SAC, DQN] across three action spaces [discretized, hybrid, continuous] over four lightweight environments [Platform, hybrid-LunarLander, Hybrid-Shoot, CoopPush]. Accounting for some invalid pairings such as joint-continuous, we are left with 220 configurations to analyze each method. We provide two new C++ parallel gymnasium and petting-zoo compliant environments [CoopPush, Hybrid-Shoot] to isolate particular challenges such as state-dependent inter-action dependence. Finally, we introduce VDN-PPO and PPO-MIX which use a branching critic to assign credit to multi-headed PPO. These variants out-perform all other tested PPO factorizations. Our results suggest that branching dueling architectures balance compute and performance most effectively, with Auto-Regressive actions reaching the highest performance overall and native continuous SAC outperforming discrete and hybrid algorithms, albiet both at increased computational cost.

Real-world online reinforcement learning (RL) provides a promising approach for training robotic manipulation policies directly in the physical world, avoiding the sim-to-real gap and enabling continuous policy refinement through human-in-the-loop interaction. Recent methods have demonstrated sample-efficient learning through human intervention but remain limited to small randomization ranges and encounter challenges with the non-stationarity induced by concurrently training multiple agents. To address these limitations, we introduce a unified framework that combines centralized training with decentralized execution (CTDE) and a Hybrid Reward Architecture (HRA). This enables multiple actors to share a centralized multi-head critic. The critic is decomposed into task and grasp heads, corresponding to the sparse task reward and a potential-based grasping reward, respectively. We accordingly reformulate the critic and actor objectives to exploit the decomposed Q-values while explicitly accounting for the categorical action distribution of the discrete gripper policy. Experimental results demonstrate that the proposed framework substantially improves both sample efficiency and policy performance. We validate our approach on two robotic arms and a simulated humanoid robot across tennis ball and banana pick-and-place, pot reset, and simulated block relocation tasks under dimension-wise domain randomization, approximately 5-25x larger than those considered in prior work. Compared with a state-of-the-art baseline, our method improves the success rate from 60% to 80% on tennis ball pick-and-place, from 60% to 90% on banana pick-and-place, and from 25% to 95% on simulated block relocation, while also successfully accomplishing a task where the baseline consistently fails. Videos and more details are available at our project website: https://hil-harc.github.io/.