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In this paper, we relate the philosophical literature on pessimism traps to information cascades, a formal model derived from the economics and mathematics literature. A pessimism trap is a social pattern in which individuals in a community, in situations of uncertainty, copy the sub-optimal actions of others, despite their individual beliefs. This maps nicely onto the concept of an information cascade, which involves a sequence of agents making a decision between two alternatives, with a private signal of the superior alternative and a public history of others' actions. Key results from the economics literature show that information cascades occur with probability one in many contexts, and depending on the strength of the signal, populations can fall into the incorrect cascade very easily and quickly. Once formed, in the absence of external perturbation, a cascade cannot be broken - therefore, we derive an intervention that can be used to nudge a population from an incorrect to a correct cascade and, importantly, maintain the cascade once the subsidy is discontinued. We extend this to the case of multiple communities, each of which might have a different optimal action, and a government providing subsidies that cannot discriminate between communities and does not know which action is optimal for each. We study this both theoretically and empirically. 

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. 

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.