Robert Schapire

Nataly Brukhim, Miroslav Dudik, Aldo Pacchiano et al.

We study an abstract framework for interactive learning called interactive estimation in which the goal is to estimate a target from its "similarity'' to points queried by the learner. We introduce a combinatorial measure called dissimilarity dimension which largely captures learnability in our model. We present a simple, general, and broadly-applicable algorithm, for which we obtain both regret and PAC generalization bounds that are polynomial in the new dimension. We show that our framework subsumes and thereby unifies two classic learning models: statistical-query learning and structured bandits. We also delineate how the dissimilarity dimension is related to well-known parameters for both frameworks, in some cases yielding significantly improved analyses.

Nived Rajaraman, Audrey Huang, Miro Dudik et al.

Chain-of-thought reasoning, where language models expend additional computation by producing thinking tokens prior to final responses, has driven significant advances in model capabilities. However, training these reasoning models is extremely costly in terms of both data and compute, as it involves collecting long traces of reasoning behavior from humans or synthetic generators and further post-training the model via reinforcement learning. Are these costs fundamental, or can they be reduced through better algorithmic design? We show that autocurriculum, where the model uses its own performance to decide which problems to focus training on, provably improves upon standard training recipes for both supervised fine-tuning (SFT) and reinforcement learning (RL). For SFT, we show that autocurriculum requires exponentially fewer reasoning demonstrations than non-adaptive fine-tuning, by focusing teacher supervision on prompts where the current model struggles. For RL fine-tuning, autocurriculum decouples the computational cost from the quality of the reference model, reducing the latter to a burn-in cost that is nearly independent of the target accuracy. These improvements arise purely from adaptive data selection, drawing on classical techniques from boosting and learning from counterexamples, and requiring no assumption on the distribution or difficulty of prompts.

Nataly Brukhim, Aldo Pacchiano, Miroslav Dudik et al.

We study the task of bandit learning, also known as best-arm identification, under the assumption that the true reward function f belongs to a known, but arbitrary, function class F. We seek a general theory of bandit learnability, akin to the PAC framework for classification. Our investigation is guided by the following two questions: (1) which classes F are learnable, and (2) how they are learnable. For example, in the case of binary PAC classification, learnability is fully determined by a combinatorial dimension - the VC dimension- and can be attained via a simple algorithmic principle, namely, empirical risk minimization (ERM). In contrast to classical learning-theoretic results, our findings reveal limitations of learning in structured bandits, offering insights into the boundaries of bandit learnability. First, for the question of "which", we show that the paradigm of identifying the learnable classes via a dimension-like quantity fails for bandit learning. We give a simple proof demonstrating that no combinatorial dimension can characterize bandit learnability, even in finite classes, following a standard definition of dimension introduced by Ben-David et al. (2019). For the question of "how", we prove a computational hardness result: we construct a reward function class for which at most two queries are needed to find the optimal action, yet no algorithm can do so in polynomial time unless RP=NP. We also prove that this class admits efficient algorithms for standard algorithmic operations often considered in learning theory, such as an ERM. This implies that computational hardness is in this case inherent to the task of bandit learning. Beyond these results, we investigate additional themes such as learning under noise, trade-offs between noise models, and the relationship between query complexity and regret minimization.

Khanh Nguyen, Dipendra Misra, Robert Schapire et al.

We present a novel interactive learning protocol that enables training request-fulfilling agents by verbally describing their activities. Unlike imitation learning (IL), our protocol allows the teaching agent to provide feedback in a language that is most appropriate for them. Compared with reward in reinforcement learning (RL), the description feedback is richer and allows for improved sample complexity. We develop a probabilistic framework and an algorithm that practically implements our protocol. Empirical results in two challenging request-fulfilling problems demonstrate the strengths of our approach: compared with RL baselines, it is more sample-efficient; compared with IL baselines, it achieves competitive success rates without requiring the teaching agent to be able to demonstrate the desired behavior using the learning agent's actions. Apart from empirical evaluation, we also provide theoretical guarantees for our algorithm under certain assumptions about the teacher and the environment.

Akshay Krishnamurthy, Thodoris Lykouris, Chara Podimata et al.

We study contextual search, a generalization of binary search in higher dimensions, which captures settings such as feature-based dynamic pricing. Standard formulations of this problem assume that agents act in accordance with a specific homogeneous response model. In practice, however, some responses may be adversarially corrupted. Existing algorithms heavily depend on the assumed response model being (approximately) accurate for all agents and have poor performance in the presence of even a few such arbitrary misspecifications. We initiate the study of contextual search when some of the agents can behave in ways inconsistent with the underlying response model. In particular, we provide two algorithms, one based on multidimensional binary search methods and one based on gradient descent. We show that these algorithms attain near-optimal regret in the absence of adversarial corruptions and their performance degrades gracefully with the number of such agents, providing the first results for contextual search in any adversarial noise model. Our techniques draw inspiration from learning theory, game theory, high-dimensional geometry, and convex analysis.

Sobhan Miryoosefi, Kianté Brantley, Hal Daumé et al.

In standard reinforcement learning (RL), a learning agent seeks to optimize the overall reward. However, many key aspects of a desired behavior are more naturally expressed as constraints. For instance, the designer may want to limit the use of unsafe actions, increase the diversity of trajectories to enable exploration, or approximate expert trajectories when rewards are sparse. In this paper, we propose an algorithmic scheme that can handle a wide class of constraints in RL tasks: specifically, any constraints that require expected values of some vector measurements (such as the use of an action) to lie in a convex set. This captures previously studied constraints (such as safety and proximity to an expert), but also enables new classes of constraints (such as diversity). Our approach comes with rigorous theoretical guarantees and only relies on the ability to approximately solve standard RL tasks. As a result, it can be easily adapted to work with any model-free or model-based RL. In our experiments, we show that it matches previous algorithms that enforce safety via constraints, but can also enforce new properties that these algorithms do not incorporate, such as diversity.

Nicole Immorlica, Karthik Abinav Sankararaman, Robert Schapire et al.

We consider Bandits with Knapsacks (henceforth, BwK), a general model for multi-armed bandits under supply/budget constraints. In particular, a bandit algorithm needs to solve a well-known knapsack problem: find an optimal packing of items into a limited-size knapsack. The BwK problem is a common generalization of numerous motivating examples, which range from dynamic pricing to repeated auctions to dynamic ad allocation to network routing and scheduling. While the prior work on BwK focused on the stochastic version, we pioneer the other extreme in which the outcomes can be chosen adversarially. This is a considerably harder problem, compared to both the stochastic version and the "classic" adversarial bandits, in that regret minimization is no longer feasible. Instead, the objective is to minimize the competitive ratio: the ratio of the benchmark reward to the algorithm's reward. We design an algorithm with competitive ratio O(log T) relative to the best fixed distribution over actions, where T is the time horizon; we also prove a matching lower bound. The key conceptual contribution is a new perspective on the stochastic version of the problem. We suggest a new algorithm for the stochastic version, which builds on the framework of regret minimization in repeated games and admits a substantially simpler analysis compared to prior work. We then analyze this algorithm for the adversarial version and use it as a subroutine to solve the latter.

Furong Huang, Jordan Ash, John Langford et al.

Deep neural networks are known to be difficult to train due to the instability of back-propagation. A deep \emph{residual network} (ResNet) with identity loops remedies this by stabilizing gradient computations. We prove a boosting theory for the ResNet architecture. We construct $T$ weak module classifiers, each contains two of the $T$ layers, such that the combined strong learner is a ResNet. Therefore, we introduce an alternative Deep ResNet training algorithm, \emph{BoostResNet}, which is particularly suitable in non-differentiable architectures. Our proposed algorithm merely requires a sequential training of $T$ "shallow ResNets" which are inexpensive. We prove that the training error decays exponentially with the depth $T$ if the \emph{weak module classifiers} that we train perform slightly better than some weak baseline. In other words, we propose a weak learning condition and prove a boosting theory for ResNet under the weak learning condition. Our results apply to general multi-class ResNets. A generalization error bound based on margin theory is proved and suggests ResNet's resistant to overfitting under network with $l_1$ norm bounded weights.

Chu Wang, Yingfei Wang, Weinan E et al.

Boosting is a generic learning method for classification and regression. Yet, as the number of base hypotheses becomes larger, boosting can lead to a deterioration of test performance. Overfitting is an important and ubiquitous phenomenon, especially in regression settings. To avoid overfitting, we consider using $l_1$ regularization. We propose a novel Frank-Wolfe type boosting algorithm (FWBoost) applied to general loss functions. By using exponential loss, the FWBoost algorithm can be rewritten as a variant of AdaBoost for binary classification. FWBoost algorithms have exactly the same form as existing boosting methods, in terms of making calls to a base learning algorithm with different weights update. This direct connection between boosting and Frank-Wolfe yields a new algorithm that is as practical as existing boosting methods but with new guarantees and rates of convergence. Experimental results show that the test performance of FWBoost is not degraded with larger rounds in boosting, which is consistent with the theoretical analysis.

Matus Telgarsky, Miroslav Dudík, Robert Schapire

This paper proves, in very general settings, that convex risk minimization is a procedure to select a unique conditional probability model determined by the classification problem. Unlike most previous work, we give results that are general enough to include cases in which no minimum exists, as occurs typically, for instance, with standard boosting algorithms. Concretely, we first show that any sequence of predictors minimizing convex risk over the source distribution will converge to this unique model when the class of predictors is linear (but potentially of infinite dimension). Secondly, we show the same result holds for \emph{empirical} risk minimization whenever this class of predictors is finite dimensional, where the essential technical contribution is a norm-free generalization bound.