This work shows that, at the inner optimum, the Hessian of the inner objective is proportional to the Fisher information matrix of the policy, yielding a structured Fisher-based hypergradient closely related to Natural Hypergradient Descent.
Abstract
Inverse reinforcement learning (IRL) aims to recover a reward function under which the resulting policy reproduces the behavior observed in expert demonstrations. A natural approach is to formulate IRL as a bilevel optimization problem, in which the inner level corresponds to policy optimization under the learned reward and the outer level measures the discrepancy between the induced policy and expert data. However, this formulation is computationally challenging in practice because the outer update requires a hypergradient involving an inverse-Hessian-vector product for the inner objective. We address this challenge by showing that, at the inner optimum, the Hessian of the inner objective is proportional to the Fisher information matrix of the policy, yielding a structured Fisher-based hypergradient closely related to Natural Hypergradient Descent. To address the resulting scalability bottleneck associated with large Fisher matrices, we approximate the required inverse-Fisher-vector product using a streaming spectral sketch, avoiding explicit construction of the Fisher matrix. We evaluate our approach against a first-order stochastic bilevel baseline across discrete- and continuous-control environments. The results demonstrate competitive policy performance and strong reward-ranking quality, while Fisher sketching reduces curvature-storage complexity and can improve computational efficiency relative to an explicit Fisher solver.
The development of safe and beneficial AI requires that systems can learn and act in accordance with human preferences. However, explicitly specifying these preferences by hand is often infeasible. Inverse reinforcement learning (IRL) addresses this challenge by inferring preferences, represented as reward functions, from expert behaviour. We introduce Q-based Variational IRL (QVIRL), a novel Bayesian IRL method that recovers a posterior distribution over rewards from expert demonstrations via primarily learning a variational distribution over optimal Q-values. Unlike previous approaches, QVIRL combines scalability with uncertainty quantification, important for safety-critical applications as well as active learning. We demonstrate QVIRL's strong performance in apprenticeship learning across various tasks, including gridworlds, Lunar Lander, the Highway Environment, and two ATARI games both with static expert data and with active learning. It is the first method for Bayesian IRL that demonstrates training from raw pixel observations.
Ondrej Bajgar, Peter Tisnikar, Alessandro Abate et al.· 0 citations
Bilevel reinforcement learning (RL) is an important framework within the literature of RL that can be used to formalize various categories of problems, such as meta-learning, hierarchical task decomposition, and reinforcement learning from human feedback (RL-HF). Most of the bilevel RL algorithms are either not scalable because of using hypergradient with Hessian, or they suffer from high sample complexity because of using penalty-based approximation methods. In this work, we propose a hypergradient-based bilevel RL algorithm using the optimality of the Boltzmann policy for the entropy regularized discounted RL objective function. Our proposed algorithm is Hessian-free and obtains an iteration complexity of $O(\epsilon^{-1})$ and state-of-the-art sample complexity of $\tilde{O}(\epsilon^{-2})$ under mild regularity conditions. Further, in our convergence analysis, we are able to remove the assumption of the Polyak-Lojasiewicz (PL) condition on the outer-level objective function present in the prior state-of-the-art sample complexity work.
Naman Saxena, Mudit Gaur, Vaneet Aggarwal· 0 citations
Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood. Building on our prior analysis (Zhu et al., 2025), we study this missing layer through the singular structure of model weights and identify spectral inheritance: RLVR can reuse the base model's weight spectra while acquiring new behavior through changes in the associated input and output singular frames. We operationalize spectral inheritance as Isospectral Optimization (ISO), an RLVR-native, fixed-spectrum optimization framework with complementary offline and online instantiations. Offline, ISO-Merger combines the frame changes of shared-base specialists into a single fixed-spectrum model, requiring no post-merge data, rollouts, gradient updates, or on-policy distillation (OPD). It recovers complementary specialist capabilities and achieves the strongest aggregate performance among the compared data-free merging methods. Online, ISO-Optimizer applies a chosen base optimizer, including AdamW and Muon, to the frame variables while keeping the base spectra fixed. Across reasoning and coding tasks ranging from 1.5B to 8B parameters, ISO-Optimizer improves accuracy in the reported runs and reaches matched scores with substantially fewer training steps. On Qwen3-8B-Base, AdamW reaches an aggregate accuracy of 0.495 after 270 training steps. ISO-AdamW reaches the same accuracy after only 100 training steps and improves further to 0.509 after 210 training steps. Together, ISO offers a concrete answer to RLVR's missing optimization layer: rather than inheriting pre-training optimization wholesale, design post-training around the structure of reward-driven adaptation: inherit the spectrum, optimize the frames.
Hanqing Zhu, Wenyan Cong, Zhizhou Sha et al.· 0 citations
Reinforcement Learning (RL) systems are typically trained using a single, well-specified scalar reward function. However, real-world decision-making tasks often involve multiple, competing objectives, such as performance versus efficiency, where ground-truth reward functions are difficult to specify or inaccessible. While Multi-Objective RL (MORL) addresses such trade-offs by modeling rewards as vectors, existing approaches typically assume access to a well-specified reward function for each objective, inheriting the same challenges faced by single-objective RL. Meanwhile, Preference-based RL (PbRL) has shown great potential in solving complex tasks without access to a pre-defined reward function through reward learning from human feedback, yet has largely been studied in single-objective settings. In this work, we bridge this gap with LEMUR: Learning to Align with Multi-Objective Reinforcement Learning with Preference feedback, a novel framework where an agent interactively learns from the preferences of multiple humans to learn optimal multi-objective policies. Our approach jointly learns policies and multiple objective-specific reward models from human feedback, enabling agents to effectively balance competing objectives during learning. We evaluate LEMUR on a variety of benchmark multi-objective tasks, and empirical results demonstrate its superior performance over baseline methods. Our method presents a promising direction for solving multi-objective decision-making tasks without pre-defined reward functions.
Manith Adikari, Bei Peng, Samuele Vinanzi et al.· 0 citations
Offline reinforcement learning (RL) aims to derive effective policies from fixed datasets without environment interaction. While generative models such as diffusion and flow matching improve policy expressiveness, they often suffer from high computational cost due to multi-step sampling and limited representational richness from uninformative Gaussian priors. To address these challenges, we propose Latent MeanFlow Policy Optimization (LaMPO), a generative policy framework that formulates offline RL as latent generative policy optimization. LaMPO learns a behavior-conditioned latent distribution, which provides an informative prior and reduces the modeling burden of the generative process. Conditioned on this prior, the MeanFlow policy is trained to predict the average action velocity, enabling high-fidelity one-step action generation that avoids the cost of iterative sampling. Guided by the MeanFlow policy, the target policy is then optimized under a MeanFlow-induced behavior constraint, achieving effective policy improvement. We further establish a theoretical performance lower bound of the target policy relative to the MeanFlow policy. Extensive evaluations across 71 tasks in OGBench, D4RL, and real-world humanoid manipulation demonstrate that LaMPO achieves superior performance with high efficiency, yielding a 19% average improvement over existing state-of-the-art methods and an 81% success rate in real-world robotic tasks.
Tenglong Liu, Xin Xu, Yixing Lan et al.· IEEE Transactions on Pattern...· 0 citations
Safe reinforcement learning maximizes reward subject to safety constraints. For Constrained Markov Decision Processes, the linear-programming view over occupancy measures implies that whenever the constraint is active at optimality, the optimal policy lies exactly on the constraint boundary, yet standard gradient-based methods do not exploit this structure and often settle in the feasible interior. We introduce Boundary-Seeking Policy Gradient (BSPG), a first-order method whose update combines a tangential component that improves reward while preserving cost to first order with a signed, residual-driven normal component that regulates the policy toward the active boundary from either side; the combined direction admits an algebraic Lagrangian form with an induced coefficient and no learned dual variable. Under exact gradients and stated regularity conditions, the constraint residual converges to zero from either side with a finite-horizon $O(1/\sqrt{T})$ bound, the tangential component is a reward-ascent direction on the boundary, and any convergent parameter sequence is stationary on the active constraint set, satisfying the KKT conditions when the limit is also a local maximizer over the feasible set. This complements existing analyses, which certify feasibility but do not characterize the constraint value at convergence. On a standard Safety-Gymnasium navigation task, BSPG attains higher reward while tracking the boundary more tightly than the compared baselines.
Chenhua Fan, Jiahui Zhu, Yuhang Zhang et al.· 0 citations