Tight bounds for strategyproof classification

In the strategyproof classication setting, a set of labeled examples is partitioned among multiple agents. Given the reported labels, an optimal classication mechanism returns a classier that minimizes the number of mislabeled exam- ples. However, each agent is interested in the accuracy of the returned classier on its own examples, and may mis- report its labels in order to achieve ...

2019 IEEE 58th Conference on Decision and Control (CDC), 2019

Motivated by applications in cyber security, we develop a simple game model for describing how a learning agent's private information influences an observing agent's inference process. The model describes a situation in which one of the agents (attacker) is deciding which of two targets to attack, one with a known reward and another with uncertain reward. The attacker receives a single private sample from the uncertain target's distribution and updates its belief of the target quality. The other agent (defender) knows the true rewards, but does not see the sample that the attacker has received. This leads to agents possessing asymmetric information: the attacker is uncertain over the parameter of the distribution, whereas the defender is uncertain about the observed sample. After the attacker updates its belief, both the attacker and the defender play a simultaneous move game based on their respective beliefs. We offer a characterization of the pure strategy equilibria of the game and explain how the players' decisions are influenced by their prior knowledge and the payoffs/costs.

SSRN Electronic Journal

We consider collective decision problems where some agents have private information about alternatives and others don't. Voting takes place under strategy-proof rules. Prior to voting, informed agents may or may not disclose their private information, thus eventually in ‡uencing the preferences of those initially uninformed. We provide general conditions on the voting rules guaranteeing that informed agents will always be induced to disclose what they know. In particular, we We thank for their comments and suggestions

ArXiv, 2021

In supervised learning, obtaining a large set of fully-labeled training data is expensive. We show that we do not always need full label information on every single training example to train a competent classifier. Specifically, inspired by the principle of sufficiency in statistics, we present a statistic (a summary) of the fully-labeled training set that captures almost all the relevant information for classification but at the same time is easier to obtain directly. We call this statistic “sufficiently-labeled data” and prove its sufficiency and efficiency for finding the optimal hidden representations, on which competent classifier heads can be trained using as few as a single randomly-chosen fully-labeled example per class. Sufficiently-labeled data can be obtained from annotators directly without collecting the fully-labeled data first. And we prove that it is easier to directly obtain sufficiently-labeled data than obtaining fully-labeled data. Furthermore, sufficiently-label...

2008

Weighted voting is a well-known model of cooperation among agents in decisionmaking domains. In such games, each player has a weight, and a coalition of players wins if its total weight meets or exceeds a given quota. Usually, the agents' power in such games is measured by a power index, such as, e.g., Shapley-Shubik index.

Proceedings of the 23rd National Conference on Artificial Intelligence Volume 1, 2008

One way for agents to reach a joint decision is to vote over the alternatives. In open, anonymous settings such as the Internet, an agent can vote more than once without being detected. A voting rule is false-name-proof if no agent ever benefits from casting additional votes. Previous work has shown that all false-name-proof voting rules are unresponsive to agents' preferences. However, that work implicitly assumes that casting additional votes is costless. In this paper, we consider what happens if there is a cost to casting additional votes. We characterize the optimal (most responsive) false-name-proofwith-costs voting rule for 2 alternatives. In sharp contrast to the costless setting, we prove that as the voting population grows larger, the probability that this rule selects the majority winner converges to 1. We also characterize the optimal group false-name-proof rule for 2 alternatives, which is robust to coalitions of agents sharing the costs of additional votes. Unfortunately, the probability that this rule chooses the majority winner as the voting population grows larger is relatively low. We derive an analogous rule in a setting with 3 alternatives, and provide bounding results and computational approaches for settings with 4 or more alternatives.

Journal of Artificial Intelligence Research, 2011

Weighted voting is a classic model of cooperation among agents in decision-making domains. In such games, each player has a weight, and a coalition of players wins the game if its total weight meets or exceeds a given quota. A player's power in such games is usually not directly proportional to his weight, and is measured by a power index, the most prominent among which are the Shapley-Shubik index and the Banzhaf index.

Computational Intelligence, 2016

Weighted voting games are important in multiagent systems because of their usage in automated decision making. However, they are not immune from the vulnerability of false-name manipulation by strategic agents that may be present in the games. False-name manipulation involves an agent splitting its weight among several false identities in anticipation of power increase. Previous works have considered false-name manipulation using the well-known Shapley-Shubik and Banzhaf power indices. Bounds on the extent of power that a manipulator may gain exist when it splits into k D 2 false identities for both the Shapley-Shubik and Banzhaf indices. The bounds when an agent splits into k > 2 false identities, until now, have remained open for the two indices. This article answers this open problem by providing four nontrivial bounds when an agent splits into k > 2 false identities for the two indices. Furthermore, we propose a new bound on the extent of power that a manipulator may gain when it splits into several false identities in a class of games referred to as excess unanimity weighted voting games. Finally, we complement our theoretical results with empirical evaluation. Results from our experiments confirm the existence of beneficial splits into several false identities for the two indices, and also establish that splitting into more than two false identities is qualitatively different than the previously known splitting into exactly two false identities.

Review of Economic Design, 2002

We calculate the proportion of preference profiles where "small" coalitions of agents may successfully manipulate any given scoring rule and show that it decreases to zero at a rate proportional to 1 √ n with the number of agents. If agents have to incur a small cost in order to decide how to manipulate the voting rule, our results imply that scoring rules are robust to such manipulation in large groups of agents. We present examples of asymptotically strategyproof and non strategyproof Condorcet consistent rules.

2019

Fairness-aware learning involves designing algorithms that do not discriminate with respect to some sensitive feature (e.g., race or gender). Existing work on the problem operates under the assumption that the sensitive feature available in one's training sample is perfectly reliable. This assumption may be violated in many real-world cases: for example, respondents to a survey may choose to conceal or obfuscate their group identity out of fear of potential discrimination. This poses the question of whether one can still learn fair classifiers given noisy sensitive features. In this paper, we answer the question in the affirmative: we show that if one measures fairness using the mean-difference score, and sensitive features are subject to noise from the mutually contaminated learning model, then owing to a simple identity we only need to change the desired fairness-tolerance. The requisite tolerance can be estimated by leveraging existing noise-rate estimators from the label noi...

2018

Peer-prediction is a mechanism which elicits privately-held, non-variable information from self-interested agents---formally, truth-telling is a strict Bayes Nash equilibrium of the mechanism. The original Peer-prediction mechanism suffers from two main limitations: (1) the mechanism must know the "common prior" of agents' signals; (2) additional undesirable and non-truthful equilibria exist which often have a greater expected payoff than the truth-telling equilibrium. A series of results has successfully weakened the known common prior assumption. However, the equilibrium multiplicity issue remains a challenge. In this paper, we address the above two problems. In the setting where a common prior exists but is not known to the mechanism we show (1) a general negative result applying to a large class of mechanisms showing truth-telling can never pay strictly more in expectation than a particular set of equilibria where agents collude to "relabel" the signals a...

2003

This paper concerns a class of collective decision-making problems under incomplete information. Members of a group receive private signals and the group must take a collective decision-e.g., make a group purchase-based on the aggregate of members' private information. Since members have diverse preferences over the outcome of this decision, each has an incentive to manipulate the decision-making process by mis-reporting his private information. Whenever there are natural bounds on the set of admissible reports-e.g., if one's signal is one's endowment, one cannot report a negative signal-an asymmetry arises between those who would over-report, and those who would under-report, their true information. To model the incentives to misreport, and the associated asymmetry, we introduce a new kind of incomplete information game called an aggregation game. In such a game, each player is characterized by two parameters: the first-the player's type-is privately known, the second is publicly observed. Players simultaneously report their types, resulting in an outcome, which is a function of the aggregate of these reports. Each player's payoff depends on his observable characteristic, the aggregate of players' type realizations and the game's outcome. Every aggregation game has a pure-strategy equilibrium. We characterize these equilibria, and study their comparative statics properties, under a variety of restrictions.

2009

We consider the problem of locating a facility on a network, represented by a graph. A set of strategic agents have different ideal locations for the facility; the cost of an agent is the distance between its ideal location and the facility. A mechanism maps the locations reported by the agents to the location of the facility. Specifically, we are interested in social choice mechanisms that do not utilize payments. We wish to design mechanisms that are strategyproof, in the sense that agents can never benefit by lying, or, even better, group strategyproof, in the sense that a coalition of agents cannot all benefit by lying. At the same time, our mechanisms must provide a small approximation ratio with respect to one of two optimization targets: the social cost or the maximum cost. We give an almost complete characterization of the feasible truthful approximation ratio under both target functions, deterministic and randomized mechanisms, and with respect to different network topologies. Our main results are: We show that a simple randomized mechanism is group strategyproof and gives a (2 − 2/n)-approximation for the social cost, where n is the number of agents, when the network is a circle (known as a ring in the case of computer networks); we design a novel "hybrid" strategyproof randomized mechanism that provides a tight approximation ratio of 3/2 for the maximum cost when the network is a circle; and we show that no randomized SP mechanism can provide an approximation ratio better than 2 − o(1) to the maximum cost even when the network is a tree, thereby matching a trivial upper bound of two.

2007

In the random assignment problem, the probabilistic serial mechanism (Bogomolnaia and Moulin 2001) is ordinally efficient and envy-free, but not strategy-proof.

Proceedings of the AAAI Conference on Artificial Intelligence

Strategic classification, i.e. classification under possible strategic manipulations of features, has received a lot of attention from both the machine learning and the game theory community. Most works focus on analysing properties of the optimal decision rule under such manipulations. In our work we take a learning theoretic perspective, focusing on the sample complexity needed to learn a good decision rule which is robust to strategic manipulation. We perform this analysis by introducing a novel loss function, the strategic manipulation loss, which takes into account both the accuracy of the final decision rule and its vulnerability to manipulation. We analyse the sample complexity for a known graph of possible manipulations in terms of the complexity of the function class and the manipulation graph. Additionally, we initialize the study of learning under unknown manipulation capabilities of the involved agents. Using techniques from transfer learning theory, we define a similari...