Best of Both Distortion Worlds

We study the problem of designing voting rules that take as input the ordinal preferences of $n$ agents over a set of $m$ alternatives and output a single alternative, aiming to optimize the overall happiness of the agents. The input to the voting rule is each agent's ranking of the alternatives from most to least preferred, yet the agents have more refined (cardinal) preferences that capture the intensity with which they prefer one alternative over another. To quantify the extent to which voting rules can optimize over the cardinal preferences given access only to the ordinal ones, prior work has used the distortion measure, i.e., the worst-case approximation ratio between a voting rule's performance and the best performance achievable given the cardinal preferences. The work on the distortion of voting rules has been largely divided into two worlds: utilitarian distortion and metric distortion. In the former, the cardinal preferences of the agents correspond to general utilities and the goal is to maximize a normalized social welfare. In the latter, the agents' cardinal preferences correspond to costs given by distances in an underlying metric space and the goal is to minimize the (unnormalized) social cost. Several deterministic and randomized voting rules have been proposed and evaluated for each of these worlds separately, gradually improving the achievable distortion bounds, but none of the known voting rules perform well in both worlds simultaneously. In this work, we prove that one can achieve the best of both worlds by designing new voting rules, that simultaneously achieve near-optimal distortion guarantees in both distortion worlds. We also prove that this positive result does not generalize to the case where the voting rule is provided with the rankings of only the top-$t$ alternatives of each agent, for $t<m$.

How Far Can I Go ? : A Self-Supervised Approach for Deterministic Video Depth Forecasting

In this paper we present a novel self-supervised method to anticipate the depth estimate for a future, unobserved real-world urban scene. This work is the first to explore self-supervised learning for estimation of monocular depth of future unobserved frames of a video. Existing works rely on a large number of annotated samples to generate the probabilistic prediction of depth for unseen frames. However, this makes it unrealistic due to its requirement for large amount of annotated depth samples of video. In addition, the probabilistic nature of the case, where one past can have multiple future outcomes often leads to incorrect depth estimates. Unlike previous methods, we model the depth estimation of the unobserved frame as a view-synthesis problem, which treats the depth estimate of the unseen video frame as an auxiliary task while synthesizing back the views using learned pose. This approach is not only cost effective - we do not use any ground truth depth for training (hence practical) but also deterministic (a sequence of past frames map to an immediate future). To address this task we first develop a novel depth forecasting network DeFNet which estimates depth of unobserved future by forecasting latent features. Second, we develop a channel-attention based pose estimation network that estimates the pose of the unobserved frame. Using this learned pose, estimated depth map is reconstructed back into the image domain, thus forming a self-supervised solution. Our proposed approach shows significant improvements in Abs Rel metric compared to state-of-the-art alternatives on both short and mid-term forecasting setting, benchmarked on KITTI and Cityscapes. Code is available at https://github.com/sauradip/depthForecasting

Two-Sided Matching Meets Fair Division

We introduce a new model for two-sided matching which allows us to borrow popular fairness notions from the fair division literature such as envy-freeness up to one good and maximin share guarantee. In our model, each agent is matched to multiple agents on the other side over whom she has additive preferences. We demand fairness for each side separately, giving rise to notions such as double envy-freeness up to one match (DEF1) and double maximin share guarantee (DMMS). We show that (a slight strengthening of) DEF1 cannot always be achieved, but in the special case where both sides have identical preferences, the round-robin algorithm with a carefully designed agent ordering achieves it. In contrast, DMMS cannot be achieved even when both sides have identical preferences.

Fair and Efficient Resource Allocation with Partial Information

We study the fundamental problem of allocating indivisible goods to agents with additive preferences. We consider eliciting from each agent only a ranking of her $k$ most preferred goods instead of her full cardinal valuations. We characterize the value of $k$ needed to achieve envy-freeness up to one good and approximate maximin share guarantee, two widely studied fairness notions. We also analyze the multiplicative loss in social welfare incurred due to the lack of full information with and without the fairness requirements.

Surprisingly Popular Voting Recovers Rankings, Surprisingly!

The wisdom of the crowd has long become the de facto approach for eliciting information from individuals or experts in order to predict the ground truth. However, classical democratic approaches for aggregating individual \emph{votes} only work when the opinion of the majority of the crowd is relatively accurate. A clever recent approach, \emph{surprisingly popular voting}, elicits additional information from the individuals, namely their \emph{prediction} of other individuals' votes, and provably recovers the ground truth even when experts are in minority. This approach works well when the goal is to pick the correct option from a small list, but when the goal is to recover a true ranking of the alternatives, a direct application of the approach requires eliciting too much information. We explore practical techniques for extending the surprisingly popular algorithm to ranked voting by partial votes and predictions and designing robust aggregation rules. We experimentally demonstrate that even a little prediction information helps surprisingly popular voting outperform classical approaches.

Learning Desirable Matchings From Partial Preferences

We study the classic problem of matching $n$ agents to $n$ objects, where the agents have ranked preferences over the objects. We focus on two popular desiderata from the matching literature: Pareto optimality and rank-maximality. Instead of asking the agents to report their complete preferences, our goal is to learn a desirable matching from partial preferences, specifically a matching that is necessarily Pareto optimal (NPO) or necessarily rank-maximal (NRM) under any completion of the partial preferences. We focus on the top-$k$ model in which agents reveal a prefix of their preference rankings. We design efficient algorithms to check if a given matching is NPO or NRM, and to check whether such a matching exists given top-$k$ partial preferences. We also study online algorithms to elicit partial preferences adaptively, and prove bounds on their competitive ratio.

Fair Algorithms for Multi-Agent Multi-Armed Bandits

We propose a multi-agent variant of the classical multi-armed bandit problem, in which there are N agents and K arms, and pulling an arm generates a (possibly different) stochastic reward to each agent. Unlike the classical multi-armed bandit problem, the goal is not to learn the "best arm", as each agent may perceive a different arm as best for her. Instead, we seek to learn a fair distribution over arms. Drawing on a long line of research in economics and computer science, we use the Nash social welfare as our notion of fairness. We design multi-agent variants of three classic multi-armed bandit algorithms, and show that they achieve sublinear regret, now measured in terms of the Nash social welfare.

Resolving the Optimal Metric Distortion Conjecture

We study the following metric distortion problem: there are two finite sets of points, V and C, that lie in the same metric space, and our goal is to choose a point in C whose total distance from the points in V is as small as possible. However, rather than having access to the underlying distance metric, we only know, for each point in V , a ranking of its distances to the points in C. We propose algorithms that choose a point in C using only these rankings as input and we provide bounds on their distortion (worst-case approximation ratio). A prominent motivation for this problem comes from voting theory, where V represents a set of voters, C represents a set of candidates, and the rankings correspond to ordinal preferences of the voters. A major conjecture in this framework is that the optimal deterministic algorithm has distortion 3. We resolve this conjecture by providing a polynomial-time algorithm that achieves distortion 3, matching a known lower bound. We do so by proving a novel lemma about matching rankings of candidates to candidates, which we refer to as the ranking-matching lemma. This lemma induces a family of novel algorithms, which may be of independent interest, and we show that a special algorithm in this family achieves distortion 3. We also provide more refined, parameterized, bounds using the notion of {\alpha}-decisiveness, which quantifies the extent to which a voter may prefer her top choice relative to all others. Finally, we introduce a new randomized algorithm with improved distortion compared to known results, and also provide improved lower bounds on the distortion of all deterministic and randomized algorithms.

Strategyproof Linear Regression in High Dimensions

This paper is part of an emerging line of work at the intersection of machine learning and mechanism design, which aims to avoid noise in training data by correctly aligning the incentives of data sources. Specifically, we focus on the ubiquitous problem of linear regression, where strategyproof mechanisms have previously been identified in two dimensions. In our setting, agents have single-peaked preferences and can manipulate only their response variables. Our main contribution is the discovery of a family of group strategyproof linear regression mechanisms in any number of dimensions, which we call generalized resistant hyperplane mechanisms. The game-theoretic properties of these mechanisms -- and, in fact, their very existence -- are established through a connection to a discrete version of the Ham Sandwich Theorem.

A Maximum Likelihood Approach For Selecting Sets of Alternatives

We consider the problem of selecting a subset of alternatives given noisy evaluations of the relative strength of different alternatives. We wish to select a k-subset (for a given k) that provides a maximum likelihood estimate for one of several objectives, e.g., containing the strongest alternative. Although this problem is NP-hard, we show that when the noise level is sufficiently high, intuitive methods provide the optimal solution. We thus generalize classical results about singling out one alternative and identifying the hidden ranking of alternatives by strength. Extensive experiments show that our methods perform well in practical settings.