A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an adversarial max-player that chooses confusing models leading to large regret. The most recent instantiation of this idea is the decision-estimation coefficient (DEC), which was shown to provide nearly tight lower and upper bounds on the worst-case expected regret in structured bandits and reinforcement learning. By re-parametrizing the offset DEC with the confidence radius and solving the corresponding min-max program, we derive an anytime variant of the Estimation-To-Decisions algorithm (Anytime-E2D).

A long line of works characterizes the sample complexity of regret minimization in sequential decision-making by min-max programs. In the corresponding saddle-point game, the min-player optimizes the sampling distribution against an adversarial max-player that chooses confusing models leading to large regret. The most recent instantiation of this idea is the decision-estimation coefficient (DEC), which was shown to provide nearly tight lower and upper bounds on the worst-case expected regret in structured bandits and reinforcement learning. By re-parametrizing the offset DEC with the confidence radius and solving the corresponding min-max program, we derive an anytime variant of the Estimation-To-Decisions algorithm (Anytime-E2D). Our formulation leads to a practical algorithm for finite model classes and linear feedback models.

The exploration of transition state (TS) geometries is crucial for elucidating chemical reaction mechanisms and modeling their kinetics. Recently, machine learning (ML) models have shown remarkable performance for prediction of TS geometries. However, they require 3D conformations of reactants and products often with their appropriate orientations as input, which demands substantial efforts and computational cost. Here, we propose a generative approach based on the stochastic diffusion method, namely TSDiff, for prediction of TS geometries just from 2D molecular graphs. TSDiff outperformed the existing ML models with 3D geometries in terms of both accuracy and efficiency. Moreover, it enables to sample various TS conformations, because it learned the distribution of TS geometries for diverse reactions in training. Thus, TSDiff was able to find more favorable reaction pathways with lower barrier heights than those in the reference database. These results demonstrate that TSDiff shows promising potential for an efficient and reliable TS exploration.

Federated learning (FL) approaches for saddle point problems (SPP) have recently gained in popularity due to the critical role they play in machine learning (ML). Existing works mostly target smooth unconstrained objectives in Euclidean space, whereas ML problems often involve constraints or non-smooth regularization, which results in a need for composite optimization. Addressing these issues, we propose Federated Dual Extrapolation (FeDualEx), an extra-step primal-dual algorithm, which is the first of its kind that encompasses both saddle point optimization and composite objectives under the FL paradigm. Both the convergence analysis and the empirical evaluation demonstrate the effectiveness of FeDualEx in these challenging settings. In addition, even for the sequential version of FeDualEx, we provide rates for the stochastic composite saddle point setting which, to our knowledge, are not found in prior literature.