Generative Adversarial Networks (GANs) have shown remarkable results in modeling complex distributions, but their evaluation remains an unsettled issue. Evaluations are essential for: (i) relative assessment of different models and (ii) monitoring the progress of a single model throughout training. The latter cannot be determined by simply inspecting the generator and discriminator loss curves as they behave non-intuitively. We leverage the notion of duality gap from game theory to propose a measure that addresses both (i) and (ii) at a low computational cost. Extensive experiments show the effectiveness of this measure to rank different GAN models and capture the typical GAN failure scenarios, including mode collapse and non-convergent behaviours. This evaluation metric also provides meaningful monitoring on the progression of the loss during training. It highly correlates with FID on natural image datasets, and with domain specific scores for text, sound and cosmology data where FID is not directly suitable. In particular, our proposed metric requires no labels or a pretrained classifier, making it domain agnostic.

We consider the problem of learning to play a repeated multi-agent game with an unknown reward function. Single player online learning algorithms attain strong regret bounds when provided with full information feedback, which unfortunately is unavailable in many real-world scenarios. Bandit feedback alone, i.e., observing outcomes only for the selected action, yields substantially worse performance. In this paper, we consider a natural model where, besides a noisy measurement of the obtained reward, the player can also observe the opponents' actions. This feedback model, together with a regularity assumption on the reward function, allows us to exploit the correlations among different game outcomes by means of Gaussian processes (GPs). We propose a novel confidence-bound based bandit algorithm GP-MW, which utilizes the GP model for the reward function and runs a multiplicative weight (MW) method. We obtain novel kernel-dependent regret bounds that are comparable to the known bounds in the full information setting, while substantially improving upon the existing bandit results. We experimentally demonstrate the effectiveness of GP-MW in random matrix games, as well as realworld problems of traffic routing and movie recommendation. In our experiments, GP-MW consistently outperforms several baselines, while its performance is often comparable to methods that have access to full information feedback.

In Interactive Machine Learning (IML), we iteratively make decisions and obtain noisy observations of an unknown function. While IML methods, e.g., Bayesian optimization and active learning, have been successful in applications, on realworld systems they must provably avoid unsafe decisions. To this end, safe IML algorithms must carefully learn about a priori unknown constraints without making unsafe decisions. Existing algorithms for this problem learn about the safety of all decisions to ensure convergence. This is sample-inefficient, as it explores decisions that are not relevant for the original IML objective.

In many machine learning applications, one needs to interactively select a sequence of items (e.g., recommending movies based on a user's feedback) or make sequential decisions in a certain order (e.g., guiding an agent through a series of states). Not only do sequences already pose a dauntingly large search space, but we must also take into account past observations, as well as the uncertainty of future outcomes. Without further structure, finding an optimal sequence is notoriously challenging, if not completely intractable. In this paper, we view the problem of adaptive and sequential decision making through the lens of submodularity and propose an adaptive greedy policy with strong theoretical guarantees. Additionally, to demonstrate the practical utility of our results, we run experiments on Amazon product recommendation and Wikipedia link prediction tasks.

How can we help a forgetful learner learn multiple concepts within a limited time frame? While there have been extensive studies in designing optimal schedules for teaching a single concept given a learner's memory model, existing approaches for teaching multiple concepts are typically based on heuristic scheduling techniques without theoretical guarantees. In this paper, we look at the problem from the perspective of discrete optimization and introduce a novel algorithmic framework for teaching multiple concepts with strong performance guarantees. Our framework is both generic, allowing the design of teaching schedules for different memory models, and also interactive, allowing the teacher to adapt the schedule to the underlying forgetting mechanisms of the learner. Furthermore, for a well-known memory model, we are able to identify a regime of model parameters where our framework is guaranteed to achieve high performance. We perform extensive evaluations using simulations along with real user studies in two concrete applications: (i) an educational app for online vocabulary teaching; and (ii) an app for teaching novices how to recognize animal species from images. Our results demonstrate the effectiveness of our algorithm compared to popular heuristic approaches.

Seeding - the task of finding initial cluster centers - is critical in obtaining highquality clusterings for k-Means. However, k-means++ seeding, the state of the art algorithm, does not scale well to massive datasets as it is inherently sequential and requires k full passes through the data. It was recently shown that Markov chain Monte Carlo sampling can be used to efficiently approximate the seeding step of k-means++. However, this result requires assumptions on the data generating distribution. We propose a simple yet fast seeding algorithm that produces provably good clusterings even without assumptions on the data. Our analysis shows that the algorithm allows for a favourable trade-off between solution quality and computational cost, speeding up k-means++ seeding by up to several orders of magnitude.

R), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds.

In classical reinforcement learning agents accept arbitrary short term loss for long term gain when exploring their environment. This is infeasible for safety critical applications such as robotics, where even a single unsafe action may cause system failure or harm the environment. In this paper, we address the problem of safely exploring finite Markov decision processes (MDP). We define safety in terms of an a priori unknown safety constraint that depends on states and actions and satisfies certain regularity conditions expressed via a Gaussian process prior.

We consider the problem of variational inference in probabilistic models with both log-submodular and log-supermodular higher-order potentials. These models can represent arbitrary distributions over binary variables, and thus generalize the commonly used pairwise Markov random fields and models with log-supermodular potentials only, for which efficient approximate inference algorithms are known. While inference in the considered models is #P-hard in general, we present efficient approximate algorithms exploiting recent advances in the field of discrete optimization. We demonstrate the effectiveness of our approach in a large set of experiments, where our model allows reasoning about preferences over sets of items with complements and substitutes.

We study a rich family of distributions that capture variable interactions significantly more expressive than those representable with low-treewidth or pairwise graphical models, or log-supermodular models. We call these cooperative graphical models. Yet, this family retains structure, which we carefully exploit for efficient inference techniques. Our algorithms combine the polyhedral structure of submodular functions in new ways with variational inference methods to obtain both lower and upper bounds on the partition function. While our fully convex upper bound is minimized as an SDP or via tree-reweighted belief propagation, our lower bound is tightened via belief propagation or mean-field algorithms. The resulting algorithms are easy to implement and, as our experiments show, effectively obtain good bounds and marginals for synthetic and real-world examples.