ARC

Compiler optimizations that execute memory accesses out of (program) order often lead to incorrect execution of concurrent programs. These re-orderings are prohibited by inserting costly fence (memory barrier) instructions. The inherent Fence Complexity is a good estimate of an algorithm's time complexity, as is its RMR complexity: the number of Remote Memory References the algorithm must issue. When write instructions are executed in order, as in the Total Store Order (TSO) model, it is possible to implement a lock (and other objects) using only one RAW fence and an optimal O(n log n) RMR complexity. However, when store instructions may be re-ordered, as in the Partial Store Order (PSO) model, we prove that there is an inherent tradeoff between fence and RMR complexities. The proof relies on an interesting encoding argument.

Networks are often naturally modeled by random processes in which nodes of the network are added one-by-one, according to some random rule. Uniform and preferential attachment trees are among the simplest examples of such dynamically growing networks. The statistical problems we address in this talk regard discovering the past of the network when a present-day snapshot is observed. Such problems are sometimes termed "network archeology". We present a few results that show that, even in gigantic networks, a lot of information is preserved from the very early days.

At the heart of Reinforcement Learning lies the challenge of trading exploration -- collecting data for identifying better models -- and exploitation -- using the estimate to make decisions. In simulated environments (e.g., games), exploration is primarily a computational concern. In real-world settings, exploration is costly, and a potentially dangerous proposition, as it requires experimenting with actions that have unknown consequences. In this talk, I will present our work towards rigorously reasoning about safety of exploration in reinforcement learning. I will discuss a model-free approach, where we seek to optimize an unknown reward function subject to unknown constraints. Both reward and constraints are revealed through noisy experiments, and safety requires that no infeasible action is chosen at any point. I will also discuss model-based approaches, where we learn about system dynamics through exploration, yet need to verify safety of the estimated policy. Our approaches use Bayesian inference over the objective, constraints and dynamics, and -- under some regularity conditions -- are guaranteed to be both safe and complete, i.e., converge to a natural notion of reachable optimum. I will also present recent results harnessing the model uncertainty for improving efficiency of exploration, and show experiments on safely and efficiently tuning cyber-physical systems in a data-driven manner.

Consider the scenario where an algorithm is given a context, and then it must select a slate of relevant results to display. As four special cases, the context may be a search query, a slot for an advertisement, a social media user, or an opportunity to show recommendations. We want to compare many alternative ranking functions that select results in different ways. However, A/B testing with traffic from real users is expensive. This research provides a method to use traffic that was exposed to a past ranking function to obtain an unbiased estimate of the utility of a hypothetical new ranking function. The method is a purely offline computation, and relies on assumptions that are quite reasonable. We show further how to design a ranking function that is the best possible, given the same assumptions. Learning optimal rankings for search results given queries is a special case. Experimental findings on data logged by a real-world e-commerce web site are positive.

Online algorithms are a hallmark of worst case optimization under uncertainty. On the other hand, in practice, the input is often far from worst case, and has some predictable characteristics. A recent line of work has shown how to use machine learned predictions to circumvent strong lower bounds on competitive ratios in classic online problems such as ski rental and caching. We study how predictive techniques can be used to break through worst case barriers in online scheduling.

The makespan minimization problem with restricted assignments is a classic problem in online scheduling theory. Worst case analysis of this problem gives Ω(log m) lower bounds on the competitive ratio in the online setting. We identify a robust quantity that can be predicted and then used to guide online algorithms to achieve better performance. Our predictions are compact in size, having dimension linear in the number of machines, and can be learned using standard off the shelf methods. The performance guarantees of our algorithms depend on the accuracy of the predictions, given predictions with error η, we show how to construct O(log η) competitive fractional assignments.

We then give an online algorithm that rounds any fractional assignment into an integral schedule. Our algorithm is O((log log m)^3)-competitive and we give a nearly matching Ω(log log m) lower bound for online rounding algorithms. Altogether, we give algorithms that, equipped with predictions with error η, achieve O(log η (log log m)^3) competitive ratios, breaking the Ω(log m) lower bound even for moderately accurate predictions.

Joint work with Thomas Lavastida, Benjamin Moseley and Sergei Vassilvitskii

We present an efficient deterministic distributed algorithm for network decomposition and explain how this implies a general distributed derandomization theorem, proving that PLOCAL=P-RLOCAL. That is, informally, any efficient (i.e., polylogarithmic-time) randomized distributed algorithm for any locally checkable graph problem can be derandomized to an efficient deterministic distributed algorithm. This leads to near-exponential improvements in deterministic and, perhaps surprisingly, randomized distributed algorithms for numerous graph problems, as well as some improvements for massively parallel algorithms (i.e., MapReduce). These results settle several decades-old and central open problems in distributed graph algorithms, including Linial's well-known MIS question [FOCS'87], which had been called the most outstanding problem in the area. This is based on joint work with my student Vaclav Rozhon.

We show that, for every epsilon>0, there is a linear programming relaxation of the Max Cut problem with at most exp(n^epsilon) variables and constraints that achieves approximation ratio at least 1/2 + delta, for some delta(epsilon)>0. Specifically, this is achieved by linear programming relaxations in the Sherali-Adams hierarchy. Previously, the only sub-exponential time algorithms known to approximate Max Cut with an approximation ratio better than 1/2 were based on semidefinite programming or spectral methods. We also provide subexponential time approximation algorithms based on linear programming for Khot's Unique Games problem, which have a qualitatively similar performance to previously known subexponential time algorithms based on spectral methods and on semidefinite programming. Joint work with Sam Hopkins and Tselil Schramm.

The privacy of personal genomic data, and how much access to it is released to commercial and non commercial entities, is an important concern. In this work, we study a specific aspect of this problem: How to determine familial, relatives relations among a large group of individuals, while keeping genomic DNA data private (or almost private). There are several commercial companies that provide such service, albeit in completely non private manner: The individual customers supply their entire genomic DNA information to these companies. We describe the moderator model, where customers keep their DNA information locally, and a central moderator matches pairs of persons who are likely to be related. These persons then engage in a secure two party computation, which checks more accurately for familial relations, and does not leak any additional information. The entire protocol leaks only a bounded amount of information to the moderator or to any other party.

Joint work with Orit Moskovich and Benny Pinkas

I will introduce a new communication model, called hybrid network, in which the nodes have the choice between two communication modes: a local mode that allows them to exchange messages with nearby nodes, and a global mode where communication between any pair of nodes is possible, but the amount of communication is limited. This can be motivated, for instance, by wireless networks in which we combine direct device-to-device communication with communication via the cellular infrastructure. I will show how to quickly build up a low-diameter, low-degree network of global edges (i.e., connections established via the global communication mode) on top of any network of local edges (i.e., connections given by the local communication mode) so that various problems such as computing minimum spanning trees and shortest paths can be solved much more efficiently than by just using the local edges.

This is joint work with various colleagues including John Augustine, Fabian Kuhn, and Mohsen Ghaffari.

Optimal Transport (OT) is a classic area in probability and statistics for transferring mass from one probability distribution to another. Recently OT has been very successfully used for domain adaptation in many applications in computer vision, texture analysis, tomographic reconstruction and clustering. We introduce a new regularizer OT which is tailored to better preserve the class structure. We give the first theoretical guarantees for an OT scheme that respects class structure. We give an accelerated proximal--projection scheme for this formulation with the proximal operator in closed form to give a highly scalable algorithm for computing optimal transport plans. Our experiments show that the new regularizer preserves class structure better and is more robust compared to previous regularizers.

I will start my talk with an introduction to the area of coresets for clustering problems, give basic definitions and explain how coresets can be used to obtain distributed and streaming algorithms. During my talk, I will mostly focus on a commonly used coreset definition that has been introduced by Har-Peled and Mazumdar: A coreset is a weighted set S of points such that for all sets C of k centers we have (1-eps) cost(P,C) <= cost(S,C) <= (1+eps) cost(P,C), where cost(P,C) is the sum of distances of the points in P to their closest center in C. Then I will present a new algorithm to compute coresets that have a similar for-all guarantee as in the above definition and that consist of a number of points that is independent of the size of the input point set P and the dimension of the input space d.

(Joint work with David Woodruff.)

In this talk I will attempt to answer the following questions I have been asked quite often: What are the current challenges in dynamic graph algorithms? What are good starting points for people who want to try working in this field? The talk will focus on challenges for basic graph problems (e.g. connectivity, shortest paths, maximum matching), and will survey some existing upper and lower bound results and techniques. [slides]