We thank all five reviewers for their detailed and incisive feedback. We tested AustereMH [16], an inexact method, on robust linear regression in Section 5.1 with N = 5000. We added this to the Appendix. R2: What if E[B] > N E[B] is typically << N, and can be decreased using small step sizes. This does not affect the properties of TunaMH.

This paper considers the problem of selecting a formula for identifying a causal quantity of interest among a set of available formulas. We assume an sequential setting in which the investigator may alter the data collection mechanism in a data-dependent way with the aim of identifying the formula with lowest asymptotic variance in as few samples as possible. We formalize this setting by using the bestarm-identification bandit framework where the standard goal of learning the arm with the lowest loss is replaced with the goal of learning the arm that will produce the best estimate. We introduce new tools for constructing finite-sample confidence bounds on estimates of the asymptotic variance that account for the estimation of potentially complex nuisance functions, and adapt the best-arm-identification algorithms of LUCB and Successive Elimination to use these bounds. We validate our method by providing upper bounds on the sample complexity and an empirical study on artificially generated data.

Each year the AAAI recognizes a group of individuals who have made significant, sustained contributions to the field of artificial intelligence by appointing them as Fellows. Over the course of the next few months, we'll be talking to some of the 2025 AAAI Fellows. In this interview we hear from Roberto Navigli, Sapienza University of Rome, who was elected as a Fellow for "significant contributions to multilingual Natural Language Understanding, and development of widely recognized methods for knowledge resource construction, text disambiguation, and semantic parsing". We find out about his career path, some big research projects he's led, and why it's important to follow your passion. My area of research is natural language processing (NLP).

Adaptive algorithms like AdaGrad and AMSGrad are successful in nonconvex optimization owing to their parameter-agnostic ability - requiring no a priori knowledge about problem-specific parameters nor tuning of learning rates. However, when it comes to nonconvex minimax optimization, direct extensions of such adaptive optimizers without proper time-scale separation may fail to work in practice. We provide such an example proving that the simple combination of Gradient Descent Ascent (GDA) with adaptive stepsizes can diverge if the primal-dual stepsize ratio is not carefully chosen; hence, a fortiori, such adaptive extensions are not parameter-agnostic. To address the issue, we formally introduce a Nested Adaptive framework, NeAda for short, that carries an inner loop for adaptively maximizing the dual variable with controllable stopping criteria and an outer loop for adaptively minimizing the primal variable. Such mechanism can be equipped with off-the-shelf adaptive optimizers and automatically balance the progress in the primal and dual variables.

Multimodal image fusion and object detection are crucial for autonomous driving. While current methods have advanced the fusion of texture details and semantic information, their complex training processes hinder broader applications. Addressing this challenge, we introduce E2E-MFD, a novel end-to-end algorithm for multimodal fusion detection.

In this supplementary material, we collect several proofs and remaining materials that are deferred from the main paper. In Appendix A, we introduce and recall necessary notations for the supplementary material. In Appendix B, we provide key lemmas and proofs for the computational complexity of robust semi-constrained optimal transport (RSOT), and those regarding ROT are in Appendix D. Appendix C is devoted to the lemmas and proofs for the computational complexity of robust semi-constrained barycenter (RSBP). We provide the proof for computational complexity of robust Sinkhorn algorithms via Nyström approximation in Appendix E. Finally, we present additional experiment studies with the proposed robust algorithms in Appendix F. This appendix aims to introduce some notations that will be used intensively in the subsequent parts of the appendix. We start with the meaning of notations for the general case, and those for remaining cases follow similarly (see the table content).

We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence.