The literature on ranking from ordinal data is vast, and there are several ways to aggregate overall preferences from pairwise comparisons between objects. In particular, it is well-known that any Nash equilibrium of the zero-sum game induced by the preference matrix defines a natural solution concept (winning distribution over objects) known as a von Neumann winner. Many real-world problems, however, are inevitably multi-criteria, with different pairwise preferences governing the different criteria. In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability. Our framework allows for non-linear aggregation of preferences across criteria, and generalizes the linearization-based approach from multi-objective optimization. From a theoretical standpoint, we show that the Blackwell winner of a multi-criteria problem instance can be computed as the solution to a convex optimization problem. Furthermore, given random samples of pairwise comparisons, we show that a simple, plug-in estimator achieves (near-)optimal minimax sample complexity. Finally, we showcase the practical utility of our framework in a user study on autonomous driving, where we find that the Blackwell winner outperforms the von Neumann winner for the overall preferences.

Additional Feedback: Some of the major/minor concerns in chronological order are as follows: 1. Please mention the citation for Condorset winner and Borda winner when you first mention them in the introduction. The authors acknowledge this aspect, anyway in the paper. In my opinion, this makes the results fairly restrictive. After the authors propose Blackwell winner, the paper's novelty seem to be fairly limited. The analysis job is well-done.

The literature on ranking from ordinal data is vast, and there are several ways to aggregate overall preferences from pairwise comparisons between objects. In particular, it is well-known that any Nash equilibrium of the zero-sum game induced by the preference matrix defines a natural solution concept (winning distribution over objects) known as a von Neumann winner. Many real-world problems, however, are inevitably multi-criteria, with different pairwise preferences governing the different criteria. In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability. Our framework allows for non-linear aggregation of preferences across criteria, and generalizes the linearization-based approach from multi-objective optimization.

The paper studied preference aggregation via pairwise comparisons along multiple criteria. All reviewers find the problem setup interesting and appreciate the theoretical contribution novelty. I also share this sentiment, and find the paper a pleasure to read. The authors are strongly encouraged to take into account the reviews, in particular, to further strengthen the empirical analysis and discussions if possible, when preparing a revision.

The literature on ranking from ordinal data is vast, and there are several ways to aggregate overall preferences from pairwise comparisons between objects. In particular, it is well-known that any Nash equilibrium of the zero-sum game induced by the preference matrix defines a natural solution concept (winning distribution over objects) known as a von Neumann winner. Many real-world problems, however, are inevitably multi-criteria, with different pairwise preferences governing the different criteria. In this work, we generalize the notion of a von Neumann winner to the multi-criteria setting by taking inspiration from Blackwell's approachability. Our framework allows for non-linear aggregation of preferences across criteria, and generalizes the linearization-based approach from multi-objective optimization.

Imitation learning (IL) is the problem of finding a policy, \(\pi\), that is as close as possible to an expert's policy, \(\pi_E\). IL algorithms can be grouped broadly into (a) online, (b) offline, and (c) interactive methods. We provide, for each setting, performance bounds for learned policies that apply for all algorithms, provably efficient algorithmic templates for achieving said bounds, and practical realizations that out-perform recent work. From beating the world champion at Go (Silver et al.) to getting cars to drive themselves (Bojarski et al.), we've seen unprecedented successes in learning to make sequential decisions over the last few years. When viewed from an algorithmic viewpoint, many of these accomplishments share a common paradigm: imitation learning (IL).

Imitation learning (IL) is the problem of finding a policy,, that is as close as possible to an expert's policy, . IL algorithms can be grouped broadly into (a) online, (b) offline, and (c) interactive methods. We provide, for each setting, performance bounds for learned policies that apply for all algorithms, provably efficient algorithmic templates for achieving said bounds, and practical realizations that out-perform recent work. From beating the world champion at Go (Silver et al.) to getting cars to drive themselves (Bojarski et al.), we've seen unprecedented successes in learning to make sequential decisions over the last few years. When viewed from an algorithmic viewpoint, many of these accomplishments share a common paradigm: imitation learning (IL).

For state-of-the-art network function virtualization (NFV) systems, it remains a key challenge to conduct effective service chain composition for different network services (NSs) with ultra-low request latencies and minimum network congestion. To this end, existing solutions often require full knowledge of the network state, while ignoring the privacy issues and overlooking the non-cooperative behaviors of users. What is more, they may fall short in the face of unexpected failures such as user unavailability and virtual machine breakdown. In this paper, we formulate the problem of service chain composition in NFV systems with failures as a non-cooperative game. By showing that such a game is a weighted potential game and exploiting the unique problem structure, we propose two effective distributed schemes that guide the service chain compositions of different NSs towards the Nash equilibrium (NE) state with both near-optimal latencies and minimum congestion.