Iterative refinement models, such as diffusion generative models and flow matching methods [Sohl-Dickstein et al., 2015, Ho et al., 2020, Song et al., 2020, Lipman et al., 2023, Albergo and V anden-Eijnden, 2023], have seen increasing popularity in recent months, and much effort has been invested

Weshowthatforpolynomial alignment, there is anover-aligned regime, in which TKRR can achieve a faster rate than what is achievable by full KRR.

Given the rich literature on random matrices, it is not surprising to find that the rank of the intermediate representations in unnormalized networks collapses quickly with depth.

This allows for local interpretation of the agent's intention based on its behavioural policy.

We study risk-sensitive reinforcement learning (RL) based on the entropic risk measure. Although existing works haveestablished non-asymptotic regret guarantees for this problem, they leave open an exponential gap between the upper and lower bounds. We identify the deficiencies in existing algorithms and their analysis that result in such a gap. To remedy these deficiencies, we investigate a simple transformation of the risk-sensitive Bellman equations, which we call theexponentialBellmanequation.