Efficient Hypergradient Descent for Inverse Reinforcement Learning

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.

Hypergradient-based Bilevel Reinforcement Learning with Improved Sample Complexity

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 $O(ε^{-1})$ and state-of-the-art sample complexity of $\tilde{O}(ε^{-2})$ 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.

On the Convergence of Self-Improving Online LLM Alignment

The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method. Empirically, SAIL has demonstrated strong performance on this task. However, a formal analysis of its convergence properties has been lacking. We identify a key theoretical challenge: the standard SAIL objective function is not guaranteed to be strongly concave due to unfavorable properties of its Hessian. To address this limitation, we propose a regularized objective, SAIL-RevKL, which incorporates a reverse Kullback-Leibler (KL) divergence penalty to improve the optimization landscape. Our central theoretical contribution is to prove that this regularized objective satisfies the Polyak-Lojasiewicz (PL) condition within a bounded parameter space. We establish global convergence guarantees, achieving a near-linear sample complexity. We further validate the effectiveness and stability of SAIL-RevKL through empirical evaluations, demonstrating that it outperforms the vanilla SAIL on both MuJoCo benchmarks and LLM alignment tasks.

Evolutionary Bilevel Reward Shaping for Generalization in Reinforcement Learning

Reinforcement learning (RL) often suffers from performance degradation when deployed in environments that differ from those encountered during training. Existing techniques such as domain randomization (DR) mitigate this, but require access to diverse training environments and full trajectory observability, assumptions that fail in privacy-preserving or restricted scenarios where only scalar performance metrics are available. We propose Generalization via Evolutionary Reward Shaping (GERS), a bilevel optimization approach to improve generalization on unseen test environments using only scalar feedback from validation environments. At the lower level, an RL agent guided via a reward function shaped by the upper level learns a policy on a limited set of training environments with accessible trajectory data; at the upper level, CMA-ES optimizes the reward shaping parameters to maximize the cumulative unshaped reward on separate validation environments for which trajectory access is unavailable. Results on continuous control tasks indicate that GERS outperforms the standard RL baseline on unseen test environments. GERS performance is comparable to DR, despite DR treating the combined set of training and validation environments of GERS as a single training set that requires trajectory access, whereas GERS cannot access validation trajectories. These results confirm that GERS effectively enhances generalization under restricted data access constraints.