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A fundamental problem in robust learning is asymmetry: a learner needs to correctly classify every one of exponentially-many perturbations that an adversary might make to a test example, but the attacker only needs to find one successful perturbation. Xiang et al. [2022] proposed an algorithm for patch attacks that reduces the effective number of perturbations from an exponential to a polynomial, and learns using an ERM oracle. However, their guarantee requires the natural examples to be robustly realizable. In this work we consider the non-robustly-realizable case. Our first contribution is to give a guarantee for this setting by utilizing an approach of Feige, Mansour, and Schapire [2015]. Next, we extend our results to a multi-group setting and introduce a novel agnostic multi-robust learning problem where the goal is to learn a predictor that achieves low robust loss on a (potentially) rich collection of subgroups. 

We study the problem of online binary classification where strategic agents can manipulate their observable features in predefined ways, modeled by a manipulation graph, in order to receive a positive classification. We show this setting differs in fundamental ways from classic (non-strategic) online classification. For instance, whereas in the non-strategic case, a mistake bound of ln |H| is achievable via the halving algorithm when the target function belongs to a known class H, we show that no deterministic algorithm can achieve a mistake bound o(Δ) in the strategic setting, where Δ is the maximum degree of the manipulation graph (even when |H| = O(Δ)). We complement this with a general algorithm achieving mistake bound O(Δ ln |H|). We also extend this to the agnostic setting, and show that this algorithm achieves a Δ multiplicative regret (mistake bound of O(Δ · OPT + Δ · ln |H|)), and that no deterministic algorithm can achieve o(Δ) multiplicative regret. Next, we study two randomized models based on whether the random choices are made before or after agents respond, and show they exhibit fundamental differences. In the first, fractional model, at each round the learner deterministically chooses a probability distribution over classifiers inducing expected values on each vertex (probabilities of being classified as positive), which the strategic agents respond to. We show that any learner in this model has to suffer linear regret. On the other hand, in the second randomized algorithms model, while the adversary who selects the next agent must respond to the learner's probability distribution over classifiers, the agent then responds to the actual hypothesis classifier drawn from this distribution. Surprisingly, we show this model is more advantageous to the learner, and we design randomized algorithms that achieve sublinear regret bounds against both oblivious and adaptive adversaries. 

In this work, we consider classification of agents who can both game and improve. For example, people wishing to get a loan may be able to take some actions that increase their perceived credit-worthiness and others that also increase their true credit-worthiness. A decision-maker would like to define a classification rule with few false-positives (does not give out many bad loans) while yielding many true positives (giving out many good loans), which includes encouraging agents to improve to become true positives if possible. We consider two models for this problem, a general discrete model and a linear model, and prove algorithmic, learning, and hardness results for each. For the general discrete model, we give an efficient algorithm for the problem of maximizing the number of true positives subject to no false positives, and show how to extend this to a partial-information learning setting. We also show hardness for the problem of maximizing the number of true positives subject to a nonzero bound on the number of false positives, and that this hardness holds even for a finite-point version of our linear model. We also show that maximizing the number of true positives subject to no false positive is NP-hard in our full linear model. We additionally provide an algorithm that determines whether there exists a linear classifier that classifies all agents accurately and causes all improvable agents to become qualified, and give additional results for low-dimensional data. 

The classical Perceptron algorithm provides a simple and elegant procedure for learning a linear classifier. In each step, the algorithm observes the sample's position and label and updates the current predictor accordingly if it makes a mistake. However, in presence of strategic agents that desire to be classified as positive and that are able to modify their position by a limited amount, the classifier may not be able to observe the true position of agents but rather a position where the agent pretends to be. Unlike the original setting with perfect knowledge of positions, in this situation the Perceptron algorithm fails to achieve its guarantees, and we illustrate examples with the predictor oscillating between two solutions forever, making an unbounded number of mistakes even though a perfect large-margin linear classifier exists. Our main contribution is providing a modified Perceptron-style algorithm which makes a bounded number of mistakes in presence of strategic agents with both $\ell_2$ and weighted $\ell_1$ manipulation costs. In our baseline model, knowledge of the manipulation costs (i.e., the extent to which an agent may manipulate) is assumed. In our most general model, we relax this assumption and provide an algorithm which learns and refines both the classifier and its cost estimates to achieve good mistake bounds even when manipulation costs are unknown. 

Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general resource allocation. Traditionally, the primary goal of such models is to maximize a linear function of the constituent matches (e.g., linear social welfare maximization) subject to some constraints. Recent work has studied a new goal of balancing whole-match diversity and economic efficiency, where the objective is instead a monotone submodular function over the matching. Basic versions of this problem are solvable in polynomial time. In this work, we prove that the problem of simultaneously maximizing diversity along several features (e.g., country of citizenship, gender, skills) is NP-hard. To address this problem, we develop the first combinatorial algorithm that constructs provably-optimal diverse b-matchings in pseudo-polynomial time. We also provide a Mixed-Integer Quadratic formulation for the same problem and show that our method guarantees optimal solutions and takes less computation time for a reviewer assignment application. The source code is made available at https://github.com/faezahmed/diverse_matching.