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Reinforcement learning in cooperative multi-agent settings has recently advanced significantly in its scope, with applications in cooperative estimation for advertising, dynamic treatment regimes, distributed control, and federated learning. In this paper, we discuss the problem of cooperative multi-agent RL with function approximation, where a group of agents communicates with each other to jointly solve an episodic MDP. We demonstrate that via careful message-passing and cooperative value iteration, it is possible to achieve near-optimal no-regret learning even with a fixed constant communication budget. Next, we demonstrate that even in heterogeneous cooperative settings, it is possible to achieve Pareto-optimal no-regret learning with limited communication. Our work generalizes several ideas from the multi-agent contextual and multi-armed bandit literature to MDPs and reinforcement learning.

Mechanism design for one-sided markets has been investigated for several decades in economics and in computer science. More recently, there has been an increased attention on mechanisms for two-sided markets, in which buyers and sellers act strategically. For two-sided markets, an impossibility result of Myerson and Satterthwaite states that no mechanism can simultaneously satisfy individual rationality (IR), incentive compatibility (IC), strong budget-balance (SBB), and be efficient. On the other hand, important applications to web advertisement, stock exchange, and frequency spectrum allocation, require us to consider two-sided combinatorial auctions in which buyers have preferences on subsets of items, and sellers may offer multiple heterogeneous items. No efficient mechanism was known so far for such two-sided combinatorial markets. This work provides the first IR, IC and SBB mechanisms that provides an O(1)-approximation to the optimal social welfare for two-sided markets. An initial construction yields such a mechanism, but exposes a conceptual problem in the traditional SBB notion. This leads us to define the stronger notion of direct trade strong budget balance (DSBB). We then proceed to design mechanisms that are IR, IC, DSBB, and again provide an O(1)-approximation to the optimal social welfare. Our mechanisms work for any number of buyers with XOS valuations - a class in between submodular and subadditive functions - and any number of sellers. We provide a mechanism that is dominant strategy incentive compatible (DSIC) if the sellers each have one item for sale, and one that is bayesian incentive compatible (BIC) if sellers hold multiple items and have additive valuations over them. Finally, we present a DSIC mechanism for the case that the valuation functions of all buyers and sellers are additive.

We consider stochastic optimization problems where a smooth (and potentially nonconvex) objective is to be minimized using a stochastic first-order oracle. These type of problems arise in many settings from simulation optimization to deep learning. We present Retrospective Approximation (RA) as a universal sequential sample-average approximation (SAA) paradigm where during each iteration $k$, a sample-path approximation problem is implicitly generated using an adapted sample size $M_k$, and solved (with prior solutions as "warm start") to an adapted error tolerance $\epsilon_k$, using a "deterministic method" such as the line search quasi-Newton method. The principal advantage of RA is that decouples optimization from stochastic approximation, allowing the direct adoption of existing deterministic algorithms without modification, thus mitigating the need to redesign algorithms for the stochastic context. A second advantage is the obvious manner in which RA lends itself to parallelization. We identify conditions on $\{M_k, k \geq 1\}$ and $\{\epsilon_k, k\geq 1\}$ that ensure almost sure convergence and convergence in $L_1$-norm, along with optimal iteration and work complexity rates. We illustrate the performance of RA with line-search quasi-Newton on an ill-conditioned least squares problem, as well as an image classification problem using a deep convolutional neural net.

In this work, we present a solution for coordinated beamforming and power allocation when base stations employ a massive number of antennas equipped with low-resolution analog-to-digital and digital-to-analog converters. We address total power minimization problems of the coarsely quantized uplink (UL) and downlink (DL) communication systems with target signal-to-interference-plus-noise ratio (SINR) constraints. By combining the UL problem with minimum mean square error combiners and deriving the Lagrangian dual of the DL problem, we prove UL-DL duality and show there is no duality gap even with coarse data converters. Inspired by strong duality, we devise an iterative algorithm to determine the optimal UL transmit powers, and then linearly amplify the UL combiners with proper weights to acquire the optimal DL precoder. Simulation results validate strong duality and evaluate the proposed method in terms of total power consumption and achieved SINR.

One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the communication matrix. This technique has two main drawbacks: it is difficult to compute, and it is not known to lower bound quantum communication complexity with entanglement. Linial and Shraibman recently introduced a norm, called gamma_2^{alpha}, to quantum communication complexity, showing that it can be used to lower bound communication with entanglement. Here the parameter alpha is a measure of approximation which is related to the allowable error probability of the protocol. This bound can be written as a semidefinite program and gives bounds at least as large as many techniques in the literature, although it is smaller than the corresponding alpha-approximation rank, rk_alpha. We show that in fact log gamma_2^{alpha}(A)$ and log rk_{alpha}(A)$ agree up to small factors. As corollaries we obtain a constant factor polynomial time approximation algorithm to the logarithm of approximate rank, and that the logarithm of approximation rank is a lower bound for quantum communication complexity with entanglement.

Most datasets of interest to the analytics industry are impacted by various forms of human bias. The outcomes of Data Analytics [DA] or Machine Learning [ML] on such data are therefore prone to replicating the bias. As a result, a large number of biased decision-making systems based on DA/ML have recently attracted attention. In this paper we introduce Rosa, a free, web-based tool to easily de-bias datasets with respect to a chosen characteristic. Rosa is based on the principles of Fair Adversarial Networks, developed by illumr Ltd., and can therefore remove interactive, non-linear, and non-binary bias. Rosa is stand-alone pre-processing step / API, meaning it can be used easily with any DA/ML pipeline. We test the efficacy of Rosa in removing bias from data-driven decision making systems by performing standard DA tasks on five real-world datasets, selected for their relevance to current DA problems, and also their high potential for bias. We use simple ML models to model a characteristic of analytical interest, and compare the level of bias in the model output both with and without Rosa as a pre-processing step. We find that in all cases there is a substantial decrease in bias of the data-driven decision making systems when the data is pre-processed with Rosa.

In the weighted bipartite matching problem, the goal is to find a maximum-weight matching in a bipartite graph with nonnegative edge weights. We consider its online version where the first vertex set is known beforehand, but vertices of the second set appear one after another. Vertices of the first set are interpreted as items, and those of the second set as bidders. On arrival, each bidder vertex reveals the weights of all adjacent edges and the algorithm has to decide which of those to add to the matching. We introduce an optimal, $e$-competitive truthful mechanism under the assumption that bidders arrive in random order (secretary model). It has been shown that the upper and lower bound of e for the original secretary problem extends to various other problems even with rich combinatorial structure, one of them being weighted bipartite matching. But truthful mechanisms so far fall short of reasonable competitive ratios once respective algorithms deviate from the original, simple threshold form. The best known mechanism for weighted bipartite matching by Krysta and V\"ocking (ICALP 2012) offers only a ratio logarithmic in the number of online vertices. We close this gap, showing that truthfulness does not impose any additional bounds. The proof technique is new in this surrounding, and based on the observation of an independency inherent to the mechanism. The insights provided hereby are interesting in their own right and appear to offer promising tools for other problems, with or without truthfulness.

Numerically computing global policies to optimal control problems for complex dynamical systems is mostly intractable. In consequence, a number of approximation methods have been developed. However, none of the current methods can quantify by how much the resulting control underperforms the elusive globally optimal solution. Here we propose policy decomposition, an approximation method with explicit suboptimality estimates. Our method decomposes the optimal control problem into lower-dimensional subproblems, whose optimal solutions are recombined to build a control policy for the entire system. Many such combinations exist, and we introduce the value error and its LQR and DDP estimates to predict the suboptimality of possible combinations and prioritize the ones that minimize it. Using a cart-pole, a 3-link balancing biped and N-link planar manipulators as example systems, we find that the estimates correctly identify the best combinations, yielding control policies in a fraction of the time it takes to compute the optimal control without a notable sacrifice in closed-loop performance. While more research will be needed to find ways of dealing with the combinatorics of policy decomposition, the results suggest this method could be an effective alternative for approximating optimal control in intractable systems.

In applications of imprecise probability, analysts must compute lower (or upper) expectations, defined as the infimum of an expectation over a set of parameter values. Monte Carlo methods consistently approximate expectations at fixed parameter values, but can be costly to implement in grid search to locate minima over large subsets of the parameter space. We investigate the use of stochastic iterative root-finding methods for efficiently computing lower expectations. In two examples we illustrate the use of various stochastic approximation methods, and demonstrate their superior performance in comparison to grid search.

In this paper, from a theoretical perspective, we study how powerful graph neural networks (GNNs) can be for learning approximation algorithms for combinatorial problems. To this end, we first establish a new class of GNNs that can solve strictly a wider variety of problems than existing GNNs. Then, we bridge the gap between GNN theory and the theory of distributed local algorithms to theoretically demonstrate that the most powerful GNN can learn approximation algorithms for the minimum dominating set problem and the minimum vertex cover problem with some approximation ratios and that no GNN can perform better than with these ratios. This paper is the first to elucidate approximation ratios of GNNs for combinatorial problems. Furthermore, we prove that adding coloring or weak-coloring to each node feature improves these approximation ratios. This indicates that preprocessing and feature engineering theoretically strengthen model capabilities.