Scaling robust robot policies requires more than broader randomization, because physical-domain experience must remain organized and learnable throughout training. We study when a policy can benefit from harder physics and identify recoverability as a central constraint in on-policy physical-domain scaling. In on-policy training, new dynamics are useful only insofar as they remain close enough to the current policy to generate corrective on-policy data, rather than collapsing rollouts into unrecoverable failures. Using quadruped locomotion as a physically demanding benchmark for embodied generalization, we introduce HORIZON, a checkpointed frontier curriculum that expands physical domains only within the current policy's recoverable boundary. HORIZON uses rollback and boundary refinement to govern each expansion step, turning fixed randomization into a continual process of physical-domain growth. Experiments reveal three regularities of physical-domain expansion. First, direct domain widening is uneven across physical axes and often unlearnable without staged ordering. Second, domain composition is non-monotonic, and adding more domains beyond a compact core can dilute recoverable joint samples and reduce overall robustness. Third, offline distillation of isolated experts cannot substitute for the joint interaction generated by on-policy curriculum. Together, these results frame physical-domain generalization as a continual growth problem for embodied control, with recoverability as the organizing principle for on-policy expansion.
Robust navigation policies for autonomous agents must generalize across continuously varying environmental conditions such as turn rates, obstacles, friction, pits, and slopes. Curriculum generation provides a principled mechanism for improving generalization by progressively adapting training environments, but designing such curricula in a sample-efficient and automated manner remains challenging. This paper proposes a reparameterized curriculum generation framework for structured continuous environment parameters using unidirectional gradient-based optimization. To improve robustness in multimodal observation spaces consisting of image-based and scalar inputs, a distribution-shift regularization objective is incorporated to encourage the learning of finer-grained latent representations. The proposed method is evaluated across two continuous-control OpenAI Gym environments: a 2D obstacle-based Car Racing variant and Bipedal Walker variant, where coupled environment parameters jointly influence policy performance. Across five random seeds, our method consistently outperforms vanilla policy training, random parameter sampling, manual curricula, frontier-based methods, Self-Paced Reinforcement Learning (SPRL), Absolute Learning Progress with Gaussian Mixture Models (ALP-GMM), and reverse curriculum learning baselines. Ablation studies further demonstrate the effectiveness of the reparameterized curriculum mechanism across both environments, while highlighting environment-dependent benefits of the auxiliary regularization objective.
Training reinforcement-learning agents directly on physical robots makes every fall costly, since a fall can damage the platform and cannot be undone like a simulator reset; the goal is therefore to minimize falls during training rather than trade them off against return, as constrained Markov decision process (MDP) formulations do. A standard mitigation hands control to a separate recovery policy whenever the agent leaves a designer-specified safe region (a subset of state space it should stay within), but the resulting mixed-policy rollouts silently bias every on-policy update, and the importance-sampling correction that would remove this bias is ill-defined whenever the recovery policy is deterministic. We address this bias with a drop-in modification of proximal policy optimization (PPO). Its core is an unbiased policy-gradient estimator that uses the score function only at safe timesteps and never evaluates the recovery policy's density, so it stays valid even when the recovery policy is deterministic, exactly where importance sampling breaks, and it empirically dominates importance sampling even when the recovery policy is stochastic. Because the recovery policy still makes credit assignment slow near the safe-region boundary, two further components accelerate learning: a closed-form value for recovery-triggering states when dynamics and recovery are deterministic, and an imitation loss that copies recovery actions only when recovery succeeds. On a three-environment, five-seed benchmark, the resulting algorithm reduces training-time falls by factors of 233x, 48x, and 26x on HalfCheetah, Ant, and Unitree Go1 over standard PPO, while matching or exceeding PPO's final reward, and on Ant, where the recovery policy is unreliable, it is the only method that reaches 80% of the best final reward.
Generalizable agents should adapt to diverse tasks and unseen environments beyond their training distribution. This position paper argues that such generalization requires environment scaling: expanding the distribution of executable rule-sets that agents interact with, rather than only increasing trajectories or tasks within fixed benchmarks. Current scaling practices largely focus on collecting more experience or broader task sets under fixed interaction rules, leaving agents brittle when underlying interfaces, dynamics, observations, or feedback signals change. The core challenge is therefore a world-level distribution shift: agents need systematic exposure to environments with meaningfully different executable rule-sets. To clarify this challenge, we propose a unified taxonomy that separates trajectory scaling, task scaling, and environment scaling by their primary deliverables and by what changes in the executable rule-set. Building on this taxonomy, we synthesize construction paradigms for scalable environments, contrasting programmatic generators that prioritize controllability and verifiability with generative world models that offer broader coverage and open-endedness. We further outline how environment scaling can be coupled with stateful learning mechanisms, emphasizing learned update rules for cross-environment adaptation. We conclude by discussing alternative perspectives and argue that scalable environments provide the essential substrate for measurable and controllable progress toward robust general agents.