Modern online platforms rely on effective rating systems to learn about items. We consider the optimal design of rating systems that collect {\em binary feedback} after transactions. We make three contributions. First, we formalize the performance of a rating system as the speed with which it recovers the true underlying ranking on items (in a large deviations sense), accounting for both items' underlying match rates and the platform's preferences. Second, we provide an efficient algorithm to compute the binary feedback system that yields the highest such performance. Finally, we show how this theoretical perspective can be used to empirically design an implementable, approximately optimal rating system, and validate our approach using real-world experimental data collected on Amazon Mechanical Turk.

In the 90s, software engineering shifted from packaged software and PCs to services and clouds, enabling distributed architectures that incorporate real-time feedback from users. In the process, digital systems became layers of technologies metricized under the authority of objective functions. These functions drive selection of software features, service integration, cloud usage, user interaction and growth, customer service, and environmental capture, among others. Whereas information systems focused on storage, processing and transport of information, and organizing knowledge --with associated risks of surveillance-- contemporary systems leverage the knowledge they gather to not only understand the world, but also to optimize it, seeking maximum extraction of economic value through the capture and manipulation of people's activities and environments. The ability of these optimization systems to treat the world not as a static place to be known, but as one to sense and co-create, poses social risks and harms such as social sorting, mass manipulation, asymmetrical concentration of resources, majority dominance, and minority erasure.

A variety of learning objectives have been proposed for training latent variable generative models. We show that many of them, including InfoGAN, ALI/BiGAN, ALICE, CycleGAN, beta-VAE, adversarial autoencoders, AVB, AS-VAE and InfoVAE, are Lagrangian duals of the same primal optimization problem, corresponding to different settings of the Lagrange multipliers. The primal problem optimizes the mutual information between latent and visible variables, subject to the constraints of accurately modeling the data distribution and performing correct amortized inference. Based on this observation, we provide an exhaustive characterization of the statistical and computational trade-offs made by all the training objectives in this class of Lagrangian duals. Next, we propose a dual optimization method where we optimize model parameters as well as the Lagrange multipliers. This method achieves Pareto near-optimal solutions in terms of optimizing information and satisfying the consistency constraints.

What are the functions of curiosity? What are the mechanisms of curiosity-driven learning? We approach these questions about the living using concepts and tools from machine learning and developmental robotics. We argue that curiosity-driven learning enables organisms to make discoveries to solve complex problems with rare or deceptive rewards. By fostering exploration and discovery of a diversity of behavioural skills, and ignoring these rewards, curiosity can be efficient to bootstrap learning when there is no information, or deceptive information, about local improvement towards these problems. We also explain the key role of curiosity for efficient learning of world models. We review both normative and heuristic computational frameworks used to understand the mechanisms of curiosity in humans, conceptualizing the child as a sense-making organism. These frameworks enable us to discuss the bi-directional causal links between curiosity and learning, and to provide new hypotheses about the fundamental role of curiosity in self-organizing developmental structures through curriculum learning. We present various developmental robotics experiments that study these mechanisms in action, both supporting these hypotheses to understand better curiosity in humans and opening new research avenues in machine learning and artificial intelligence. Finally, we discuss challenges for the design of experimental paradigms for studying curiosity in psychology and cognitive neuroscience. Keywords: Curiosity, intrinsic motivation, lifelong learning, predictions, world model, rewards, free-energy principle, learning progress, machine learning, AI, developmental robotics, development, curriculum learning, self-organization.

We consider the problem of automated assignment of papers to reviewers in conference peer review, with a focus on fairness and statistical accuracy. Our fairness objective is to maximize the review quality of the most disadvantaged paper, in contrast to the commonly used objective of maximizing the total quality over all papers. We design an assignment algorithm based on an incremental max-flow procedure that we prove is near-optimally fair. Our statistical accuracy objective is to ensure correct recovery of the papers that should be accepted. We provide a sharp minimax analysis of the accuracy of the peer-review process for a popular objective-score model as well as for a novel subjective-score model that we propose in the paper. Our analysis proves that our proposed assignment algorithm also leads to a near-optimal statistical accuracy. Finally, we design a novel experiment that allows for an objective comparison of various assignment algorithms, and overcomes the inherent difficulty posed by the absence of a ground truth in experiments on peer-review. The results of this experiment corroborate the theoretical guarantees of our algorithm.

Design optimization techniques are often used at the beginning of the design process to explore the space of possible designs. In these domains illumination algorithms, such as MAP-Elites, are promising alternatives to classic optimization algorithms because they produce diverse, high-quality solutions in a single run, instead of only a single near-optimal solution. Unfortunately, these algorithms currently require a large number of function evaluations, limiting their applicability. In this article we introduce a new illumination algorithm, Surrogate-Assisted Illumination (SAIL), that leverages surrogate modeling techniques to create a map of the design space according to user-defined features while minimizing the number of fitness evaluations. On a 2-dimensional airfoil optimization problem SAIL produces hundreds of diverse but high-performing designs with several orders of magnitude fewer evaluations than MAP-Elites or CMA-ES. We demonstrate that SAIL is also capable of producing maps of high-performing designs in realistic 3-dimensional aerodynamic tasks with an accurate flow simulation. Data-efficient design exploration with SAIL can help designers understand what is possible, beyond what is optimal, by considering more than pure objective-based optimization.

This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with polynomial time-complexity with respect to the number of data can be devised for robust regression and subspace estimation. This result is obtained by adopting a classification point of view and relating the problems to the search for a linear model that can approximate the maximal number of points with a given error. Approximate variants of the algorithms based on ramdom sampling are also discussed and experiments show that it offers an accuracy gain over the traditional RANSAC for a similar algorithmic simplicity.

We consider the problem of learning a low-rank matrix, constrained to lie in a linear subspace, and introduce a novel factorization for modeling such matrices. A salient feature of the proposed factorization scheme is it decouples the low-rank and the structural constraints onto separate factors. We formulate the optimization problem on the Riemannian spectrahedron manifold, where the Riemannian framework allows to develop computationally efficient conjugate gradient and trust-region algorithms. Experiments on problems such as standard/robust/nonnegative matrix completion, Hankel matrix learning and multi-task learning demonstrate the efficacy of our approach. A shorter version of this work has been published in ICML'18 (Jawanpuria and Mishra, 2018).

It has recently been shown that the problem of testing global convexity of polynomials of degree four is {strongly} NP-hard, answering an open question of N.Z. Shor. This result is minimal in the degree of the polynomial when global convexity is of concern. In a number of applications however, one is interested in testing convexity only over a compact region, most commonly a box (i.e., hyper-rectangle). In this paper, we show that this problem is also strongly NP-hard, in fact for polynomials of degree as low as three. This result is minimal in the degree of the polynomial and in some sense justifies why convexity detection in nonlinear optimization solvers is limited to quadratic functions or functions with special structure. As a byproduct, our proof shows that the problem of testing whether all matrices in an interval family are positive semidefinite is strongly NP-hard. This problem, which was previously shown to be (weakly) NP-hard by Nemirovski, is of independent interest in the theory of robust control.

In this paper, we provide two new stable online algorithms for the problem of prediction in reinforcement learning, \emph{i.e.}, estimating the value function of a model-free Markov reward process using the linear function approximation architecture and with memory and computation costs scaling quadratically in the size of the feature set. The algorithms employ the multi-timescale stochastic approximation variant of the very popular cross entropy (CE) optimization method which is a model based search method to find the global optimum of a real-valued function. A proof of convergence of the algorithms using the ODE method is provided. We supplement our theoretical results with experimental comparisons. The algorithms achieve good performance fairly consistently on many RL benchmark problems with regards to computational efficiency, accuracy and stability.