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We consider the vulnerability of fairness-constrained learning to malicious noise in the training data. Konstantinov and Lampert (2021) initiated the study of this question and proved that any proper learner can exhibit high vulnerability when group sizes are imbalanced. Here, we present a more optimistic view, showing that if we allow randomized classifiers, then the landscape is much more nuanced. For example, for Demographic Parity we need only incur a Θ(α) loss in accuracy, where α is the malicious noise rate, matching the best possible even without fairness constraints. For Equal Opportunity, we show we can incur an O(sqrt(α)) loss, and give a matching Ω(sqrt(α)) lower bound. For Equalized Odds and Predictive Parity, however, and adversary can indeed force an Ω(1) loss. The key technical novelty of our work is how randomization can bypass simple 'tricks' an adversary can use to amplify its power. These results provide a more fine-grained view of the sensitivity of fairness-constrained learning to adversarial noise in training data. 

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 introduce and study the problem of dueling optimization with a monotone adversary, a generalization of (noiseless) dueling convex optimization. The goal is to design an online algorithm to find a minimizer x* for a function f:X→R, for X \subseteq R^d. In each round, the algorithm submits a pair of guesses x1 and x2, and the adversary responds with any point in the space that is at least as good as both guesses. The cost of each query is the suboptimality of the worst of the two guesses; i.e., max(f(x1) − f(x*),f(x2) − f(x*)). The goal is to minimize the number of iterations required to find an ε-optimal point and to minimize the total cost (regret) of the guesses over many rounds. Our main result is an efficient randomized algorithm for several natural choices of the function f and set X that incurs cost O(d) and iteration complexity O(d log(1/ε)^2). Moreover, our dependence on d is asymptotically optimal, as we show examples in which any randomized algorithm for this problem must incur Ω(d) cost and iteration complexity. 

Gameplay under various forms of uncertainty has been widely studied. Feldman et al. [Michal Feldman et al., 2010] studied a particularly low-information setting in which one observes the opponent’s actions but no payoffs, not even one’s own, and introduced an algorithm which guarantees one’s payoff nonetheless approaches the minimax optimal value (i.e., zero) in a symmetric zero-sum game. Against an opponent playing a minimax-optimal strategy, approaching the value of the game is the best one can hope to guarantee. However, a wealth of research in behavioral economics shows that people often do not make perfectly rational, optimal decisions. Here we consider whether it is possible to actually win in this setting if the opponent is behaviorally biased. We model several deterministic, biased opponents and show that even without knowing the game matrix in advance or observing any payoffs, it is possible to take advantage of each bias in order to win nearly every round (so long as the game has the property that each action beats and is beaten by at least one other action). We also provide a partial characterization of the kinds of biased strategies that can be exploited to win nearly every round, and provide algorithms for beating some kinds of biased strategies even when we don't know which strategy the opponent uses. 

We consider strategic classification, where agents can strategically manipulate their feature vector to a limited extent in order to be classified as positive. Unlike most prior work, our work considers manipulations to be personalized, meaning that agents can have different levels of manipulation abilities (e.g., varying radii for ball manipulations), and unknown to the learner. We formalize the learning problem in an interaction model where the learner first deploys a classifier and the agent manipulates the feature vector within their manipulation set to game the deployed classifier. We investigate various scenarios in terms of the information available to the learner during the interaction, such as observing the original feature vector before or after deployment, observing the manipulated feature vector, or not seeing either the original or the manipulated feature vector, and provide online mistake bounds and PAC sample complexity in these scenarios for ball manipulations. 

In this work, we propose a multi-objective decision making framework that accommodates different user preferences over objectives, where preferences are learned via policy comparisons. Our model consists of a known Markov decision process with a vector-valued reward function, with each user having an unknown preference vector that expresses the relative importance of each objective. The goal is to efficiently compute a near-optimal policy for a given user. We consider two user feedback models. We first address the case where a user is provided with two policies and returns their preferred policy as feedback. We then move to a different user feedback model, where a user is instead provided with two small weighted sets of representative trajectories and selects the preferred one. In both cases, we suggest an algorithm that finds a nearly optimal policy for the user using a number of comparison queries that scales quasilinearly in the number of objectives. 

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.