Off-policy evaluation (OPE) is the problem of estimating the expected return in an unknown Markov decision process (MDP) of a given decision policy, known as the evaluation policy, using transition data generated by another policy, known as the behavior policy (Bibaut et al., 2019; Precup et al., 2000; Thomas et al., 2015). OPE is especially important in applications where experimentation is particularly costly, such as in medicine. Recently, the first-order efficiency bound for OPE was derived by Kallus and Uehara (2020) for time-varying MDPs and by Kallus and Uehara (2019) for time-homogeneous MDPs (which we focus on and simply call MDPs). That is, the smallest-possible coefficient of the leading 1/ n term C in the estimation error C/ n o(1/ n). In the time-varying tabular setting, the bounds coincides with that of Jiang and Li (2016), and Yin and Wang (2020) showed that the model-based estimator achieves it. However, the achievability of the lower bound in general settings is unclear. Among the approaches to OPE, many of them rely on estimating the q-function (representing long-term value) or the w-function (representing density ratios), under the so-called realizability (a.k.a well-specification) and/or completeness (a.k.a hypothesis class closed under Bellman operators; Antos et al., 2008; Chen and Jiang, 2019) assumptions. For example, the q-function can be estimated via Fitted-Q Iteration (FQI; Ernst et al., 2005), and the w-function is central to recent methods based on the idea of marginalized importance sampling (Gelada and Bellemare, 2019; Liu et al., 2018). In this paper, we study minimax estimators of q-and w-functions and its implications for OPE.

In this work we consider multitasking in the context of solving multiple optimization problems simultaneously by conducting a single search process. The principal goal when dealing with this scenario is to dynamically exploit the existing complementarities among the problems (tasks) being optimized, helping each other through the exchange of valuable knowledge. Additionally, the emerging paradigm of Evolutionary Multitasking tackles multitask optimization scenarios by using as inspiration concepts drawn from Evolutionary Computation. The main purpose of this survey is to collect, organize and critically examine the abundant literature published so far in Evolutionary Multitasking, with an emphasis on the methodological patterns followed when designing new algorithmic proposals in this area (namely, multifactorial optimization and multipopulation-based multitasking). We complement our critical analysis with an identification of challenges that remain open to date, along with promising research directions that can stimulate future efforts in this topic. Our discussions held throughout this manuscript are offered to the audience as a reference of the general trajectory followed by the community working in this field in recent times, as well as a self-contained entry point for newcomers and researchers interested to join this exciting research avenue.

While algorithm audits are growing rapidly in commonality and public importance, relatively little scholarly work has gone toward synthesizing prior work and strategizing future research in the area. This systematic literature review aims to do just that, following PRISMA guidelines in a review of over 500 English articles that yielded 62 algorithm audit studies. The studies are synthesized and organized primarily by behavior (discrimination, distortion, exploitation, and misjudgement), with codes also provided for domain (e.g. search, vision, advertising, etc.), organization (e.g. Google, Facebook, Amazon, etc.), and audit method (e.g. sock puppet, direct scrape, crowdsourcing, etc.). The review shows how previous audit studies have exposed public-facing algorithms exhibiting problematic behavior, such as search algorithms culpable of distortion and advertising algorithms culpable of discrimination. Based on the studies reviewed, it also suggests some behaviors (e.g. discrimination on the basis of intersectional identities), domains (e.g. advertising algorithms), methods (e.g. code auditing), and organizations (e.g. Twitter, TikTok, LinkedIn) that call for future audit attention. The paper concludes by offering the common ingredients of successful audits, and discussing algorithm auditing in the context of broader research working toward algorithmic justice.

Wasserstein barycenters provide a geometric notion of the weighted average of probability measures based on optimal transport. In this paper, we present a scalable algorithm to compute Wasserstein-2 barycenters given sample access to the input measures, which are not restricted to being discrete. While past approaches rely on entropic or quadratic regularization, we employ input convex neural networks and cycle-consistency regularization to avoid introducing bias. As a result, our approach does not resort to minimax optimization. We provide theoretical analysis on error bounds as well as empirical evidence of the effectiveness of the proposed approach in low-dimensional qualitative scenarios and high-dimensional quantitative experiments.

Stackelberg equilibrium is a solution concept in two-player games where the leader has commitment rights over the follower. In recent years, it has become a cornerstone of many security applications, including airport patrolling and wildlife poaching prevention. Even though many of these settings are sequential in nature, existing techniques pre-compute the entire solution ahead of time. In this paper, we present a theoretically sound and empirically effective way to apply search, which leverages extra online computation to improve a solution, to the computation of Stackelberg equilibria in general-sum games. Instead of the leader attempting to solve the full game upfront, an approximate "blueprint" solution is first computed offline and is then improved online for the particular subgames encountered in actual play. We prove that our search technique is guaranteed to perform no worse than the pre-computed blueprint strategy, and empirically demonstrate that it enables approximately solving significantly larger games compared to purely offline methods. We also show that our search operation may be cast as a smaller Stackelberg problem, making our method complementary to existing algorithms based on strategy generation.

Which classes can be learned properly in the online model? -- that is, by an algorithm that at each round uses a predictor from the concept class. While there are simple and natural cases where improper learning is necessary, it is natural to ask how complex must the improper predictors be in such cases. Can one always achieve nearly optimal mistake/regret bounds using "simple" predictors? In this work, we give a complete characterization of when this is possible, thus settling an open problem which has been studied since the pioneering works of Angluin (1987) and Littlestone (1988). More precisely, given any concept class C and any hypothesis class H, we provide nearly tight bounds (up to a log factor) on the optimal mistake bounds for online learning C using predictors from H. Our bound yields an exponential improvement over the previously best known bound by Chase and Freitag (2020). As applications, we give constructive proofs showing that (i) in the realizable setting, a near-optimal mistake bound (up to a constant factor) can be attained by a sparse majority-vote of proper predictors, and (ii) in the agnostic setting, a near-optimal regret bound (up to a log factor) can be attained by a randomized proper algorithm. A technical ingredient of our proof which may be of independent interest is a generalization of the celebrated Minimax Theorem (von Neumann, 1928) for binary zero-sum games. A simple game which fails to satisfy Minimax is "Guess the Larger Number", where each player picks a number and the larger number wins. The payoff matrix is infinite triangular. We show this is the only obstruction: if a game does not contain triangular submatrices of unbounded sizes then the Minimax Theorem holds. This generalizes von Neumann's Minimax Theorem by removing requirements of finiteness (or compactness), and captures precisely the games of interest in online learning.

Program synthesis is an active research field in academia, national labs, and industry. Yet, work directly applicable to scientific computing, while having some impressive successes, has been limited. This report reviews the relevant areas of program synthesis work for scientific computing, discusses successes to date, and outlines opportunities for future work. This report is the result of the Workshop on Program Synthesis for Scientific Computing was held virtually on August 4-5 2020 (https://prog-synth-science.github.io/2020/).

The idea is to minimize the occurrence of multiple objects from the same cluster in the same set. In the current paper, we study computational aspects of the method. First, we prove that the problem of finding the optimal clustering is NP-hard. Second, to numerically find a suitable clustering, we propose to use the genetic algorithm augmented by a renumbering procedure, a fast task-specific local search heuristic and an initial solution based on a simplified model. Third, in a simulation study, we demonstrate that our improvements of the standard genetic algorithm significantly enhance its computational performance.

In many risk-aware and multi-objective reinforcement learning settings, the utility of the user is derived from the single execution of a policy. In these settings, making decisions based on the average future returns is not suitable. For example, in a medical setting a patient may only have one opportunity to treat their illness. When making a decision, just the expected return -- known in reinforcement learning as the value -- cannot account for the potential range of adverse or positive outcomes a decision may have. Our key insight is that we should use the distribution over expected future returns differently to represent the critical information that the agent requires at decision time. In this paper, we propose Distributional Monte Carlo Tree Search, an algorithm that learns a posterior distribution over the utility of the different possible returns attainable from individual policy executions, resulting in good policies for both risk-aware and multi-objective settings. Moreover, our algorithm outperforms the state-of-the-art in multi-objective reinforcement learning for the expected utility of the returns.

The Rubik's Cube has been around for decades. I've toyed with the cube, probably in the very late '80s or early '90s, but never even imagined being able to solve one; from entirely shuffled, to perfectly ordered. But wouldn't it be satisfying if I could? Fortunately, the internet makes solving what was originally an architecture puzzle, doable for most of us. The world record for solving a cube has plummeted since 2000 from 20 seconds to under five, as pros and enthusiasts synthesized high-speed solutions and turn combinations (called algorithms) and shared them with the world.