AI 速览：作者证明不可知学习与多准确度（生成式不可区分）任务在计算复杂度上等价，并给出从多准确度到不可知学习的高效归约。
Given a class of machine learning models and sample access to a data distribution with binary labels, which computational task is harder: training a discriminative model that distinguishes positive and negative labels as well as the best member of the class, or training a generative model whose outputs are indistinguishable from real data by all members of the class? We prove that these two fundamental tasks in computational learning theory are not just closely related, but actually equivalent to each other in complexity. One direction of this equivalence was previously known. Indeed, the powerful regularity lemma in complexity theory gives an efficient oracle reduction from the indistinguishability task (a.k.a. multiaccuracy) to the distinguishing task (a.k.a. agnostic learning) in the style of boosting algorithms. Our main contribution is an efficient oracle reduction in the other direction. Taking this idea further, we show that a multiaccuracy oracle is a remarkably powerful primitive, achieving not just agnostic learning but also a wide range of seemingly more demanding learning objectives via similarly efficient and direct constructions. Our results crucially use the power of making adaptive queries to the oracle, and stand in stark contrast to prior work, which showed that post-processing a single multiaccurate predictor is insufficient for even weak forms of learning. On a technical level, we draw a connection between our (offline) problem and a version of no-regret learning in the online setting, which allows us to use follow-the-leader type algorithms to modify the label distribution and aggregate the predictions of the multiaccuracy oracle.
AI 速览：作者通过凸对偶将硬核引理推广为基于掩蔽信道保真度的通用硬度认证框架，覆盖非布尔函数与多种损失。
We prove a broad learning-theoretic generalization of the celebrated hardcore lemma concerning the average-case complexity of computing a Boolean function (Impagliazzo, 1995). Our starting point is the observation that the classic notion of a hardcore measure, which reweights a function's input distribution, is equivalent to an input-dependent masking channel that injects randomness into the function's output distribution until it appears fully pseudorandom. The analogue of density of the measure is the fidelity of the channel. From this viewpoint, we develop a general framework for certifying hardness that allows for non-Boolean functions $f$ and a wide range of notions of hardness besides the classic 0-1 loss, by choosing the right notion of fidelity via convex duality. We show the difficulty of learning $f$ using a class $\mathcal{C}$ to minimize a convex loss is tightly characterized by the maximum fidelity possible for a masking channel, which measures the least amount of noise the channel must add to hide the structure of $f$ and make it $\mathcal{C}$-indistinguishable from random noise. Using our framework, we derive a number of multiclass generalizations of the hardcore lemma, and reveal some unexpected subtleties in going to larger alphabets. We construct a universal masking channel that applies to many natural notions of hardness simultaneously. Such channels are dual to omnipredictors, which optimize multiple losses at once (Gopalan, Kalai, Reingold, Sharan, and Wieder, 2022). We observe a symmetry between masking channels and generalizations of the hardcore lemma using pseudoentropy. We present a tight characterization of pseudoentropy using the MaxEnt algorithm from machine learning. A long line of research has shown that learning and hardness are two sides of the same coin; our framework gives a crisp and general formulation of this principle via convex duality.