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This paper extends certification methods to risk-sensitive reinforcement learning, establishing lower bounds on expected rewards under state adversarial perturbations via convex optimization and demonstrating improved certified bounds with risk-averse training.
This paper proves that a single normalized nonnegative kernel-attention head requires exponentially many features to solve a simple Min-IP task on three-token sequences, whereas dense softmax attention solves it with constant temperature and m-dimensional scores, highlighting a fundamental expressive-power gap between kernel and full attention.
This paper proves sharp dimension-free first-order lower bounds for finding epsilon-stationary points in higher-order smooth nonconvex optimization, resolving open problems for Hessian-Lipschitz and third-order smooth cases.
This paper studies risk-sensitive reinforcement learning in finite discounted MDPs with a generative model, focusing on the sample complexity of learning optimal value functions and policies under the optimized certainty equivalent (OCE) risk measure. It provides exact conditions for PAC-learnability, analyzes a model-based approach, and establishes tight lower bounds, including an improved dependence on the risk parameter for CVaR.