The choice of the control frequency of a system has a relevant impact on the ability of reinforcement learning algorithms to learn a highly performing policy. In this paper, we introduce the notion of action persistence that consists in the repetition of an action for a fixed number of decision steps, having the effect of modifying the control frequency. We start analyzing how action persistence affects the performance of the optimal policy, and then we present a novel algorithm, Persistent Fitted Q-Iteration (PFQI), that extends FQI, with the goal of learning the optimal value function at a given persistence. After having provided a theoretical study of PFQI and a heuristic approach to identify the optimal persistence, we present an experimental campaign on benchmark domains to show the advantages of action persistence and proving the effectiveness of our persistence selection method.

Can deep neural networks learn to solve any task, and in particular problems of high complexity? This question attracts a lot of interest, with recent works tackling computationally hard tasks such as the traveling salesman problem and satisfiability. In this work we offer a different perspective on this question. Given the common assumption that NP != coNP we prove that any polynomial-time sample generator for an NP-hard problem samples, in fact, from an easier sub-problem. We empirically explore a case study, Conjunctive Query Containment, and show how common data generation techniques generate biased data-sets that lead practitioners to over-estimate model accuracy. Our results suggest that machine learning approaches that require training on a dense uniform sampling from the target distribution cannot be used to solve computationally hard problems, the reason being the difficulty of generating sufficiently large and unbiased training sets.

Gaussian processes (GPs) are nonparametric Bayesian models that have been applied to regression and classification problems. One of the approaches to alleviate their cubic training cost is the use of local GP experts trained on subsets of the data. In particular, product-of-expert models combine the predictive distributions of local experts through a tractable product operation. While these expert models allow for massively distributed computation, their predictions typically suffer from erratic behaviour of the mean or uncalibrated uncertainty quantification. By calibrating predictions via a tempered softmax weighting, we provide a solution to these problems for multiple product-of-expert models, including the generalised product of experts and the robust Bayesian committee machine. Furthermore, we leverage the optimal transport literature and propose a new product-of-expert model that combines predictions of local experts by computing their Wasserstein barycenter, which can be applied to both regression and classification.

We report a series of robust empirical observations, demonstrating that deep Neural Networks learn the examples in both the training and test sets in a similar order. This phenomenon is observed in all the commonly used benchmarks we evaluated, including many image classification benchmarks, and one text classification benchmark. While this phenomenon is strongest for models of the same architecture, it also crosses architectural boundaries -- models of different architectures start by learning the same examples, after which the more powerful model may continue to learn additional examples. We further show that this pattern of results reflects the interplay between the way neural networks learn benchmark datasets. Thus, when fixing the architecture, we show synthetic datasets where this pattern ceases to exist. When fixing the dataset, we show that other learning paradigms may learn the data in a different order. We hypothesize that our results reflect how neural networks discover structure in natural datasets.

We present an extension to the disjoint paths problem in which additional lifted edges are introduced to provide path connectivity priors. We call the resulting optimization problem the lifted disjoint paths problem. We show that this problem is NP-hard by reduction from integer multicommodity flow and 3-SAT. To enable practical global optimization, we propose several classes of linear inequalities that produce a high-quality LP-relaxation. Additionally, we propose efficient cutting plane algorithms for separating the proposed linear inequalities. The lifted disjoint path problem is a natural model for multiple object tracking and allows an elegant mathematical formulation for long range temporal interactions. Lifted edges help to prevent id switches and to re-identify persons. Our lifted disjoint paths tracker achieves nearly optimal assignments with respect to input detections. As a consequence, it leads on all three main benchmarks of the MOT challenge, improving significantly over state-of-the-art.

Model-free reinforcement learning is known to be memory and computation efficient and more amendable to large scale problems. In this paper, two model-free algorithms are introduced for learning infinite-horizon average-reward Markov Decision Processes (MDPs). The first algorithm reduces the problem to the discounted-reward version and achieves $\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of weakly communicating MDPs. To our knowledge, this is the first model-free algorithm for general MDPs in this setting. The second algorithm makes use of recent advances in adaptive algorithms for adversarial multi-armed bandits and improves the regret to $\mathcal{O}(\sqrt{T})$, albeit with a stronger ergodic assumption. This result significantly improves over the $\mathcal{O}(T^{3/4})$ regret achieved by the only existing model-free algorithm by Abbasi-Yadkori et al. (2019) for ergodic MDPs in the infinite-horizon average-reward setting.

Highly overparametrized neural networks can display curiously strong generalization performance -- a phenomenon that has recently garnered a wealth of theoretical and empirical research in order to better understand it. In contrast to most previous work, which typically considers the performance as a function of the model size, in this paper we empirically study the generalization performance as the size of the training set varies over multiple orders of magnitude. These systematic experiments lead to some interesting and potentially very useful observations; perhaps most notably that training on smaller subsets of the data can lead to more reliable model selection decisions whilst simultaneously enjoying smaller computational overheads. Our experiments furthermore allow us to estimate Minimum Description Lengths for common datasets given modern neural network architectures, thereby paving the way for principled model selection taking into account Occams-razor.

We propose an accelerated version of stochastic variance reduced coordinate descent -- ASVRCD. As other variance reduced coordinate descent methods such as SEGA or SVRCD, our method can deal with problems that include a non-separable and non-smooth regularizer, while accessing a random block of partial derivatives in each iteration only. However, ASVRCD incorporates Nesterov's momentum, which offers favorable iteration complexity guarantees over both SEGA and SVRCD. As a by-product of our theory, we show that a variant of Katyusha (Allen-Zhu, 2017) is a specific case of ASVRCD, recovering the optimal oracle complexity for the finite sum objective.

Model-based reinforcement learning approaches leverage a forward dynamics model to support planning and decision making, which, however, may fail catastrophically if the model is inaccurate. Although there are several existing methods dedicated to combating the model error, the potential of the single forward model is still limited. In this paper, we propose to additionally construct a backward dynamics model to reduce the reliance on accuracy in forward model predictions. We develop a novel method, called Bidirectional Model-based Policy Optimization (BMPO) to utilize both the forward model and backward model to generate short branched rollouts for policy optimization. Furthermore, we theoretically derive a tighter bound of return discrepancy, which shows the superiority of BMPO against the one using merely the forward model. Extensive experiments demonstrate that BMPO outperforms state-of-the-art model-based methods in terms of sample efficiency and asymptotic performance.

In this paper, we propose a boosting algorithm for regression problems called \textit{boosted histogram transform for regression} (BHTR) based on histogram transforms composed of random rotations, stretchings, and translations. From the theoretical perspective, we first prove fast convergence rates for BHTR under the assumption that the target function lies in the spaces $C^{0,\alpha}$. Moreover, if the target function resides in the subspace $C^{1,\alpha}$, by establishing the upper bound of the convergence rate for the boosted regressor, i.e. BHTR, and the lower bound for base regressors, i.e. histogram transform regressors (HTR), we manage to explain the benefits of the boosting procedure. In the experiments, compared with other state-of-the-art algorithms such as gradient boosted regression tree (GBRT), Breiman's forest, and kernel-based methods, our BHTR algorithm shows promising performance on both synthetic and real datasets.

We describe a framework for constructing nonstationary nonseparable random fields based on an infinite mixture of convolved stochastic processes. When the mixing process is stationary but the convolution function is nonstationary we arrive at nonseparable kernels with constant non-separability that are available in closed form. When the mixing is nonstationary and the convolution function is stationary we arrive at nonseparable random fields that have varying nonseparability and better preserve local structure. These fields have natural interpretations through the spectral representation of stochastic differential equations (SDEs) and are demonstrated on a range of synthetic benchmarks and spatio-temporal applications in geostatistics and machine learning. We show how a single Gaussian process (GP) with these random fields can computationally and statistically outperform both separable and existing nonstationary nonseparable approaches such as treed GPs and deep GP constructions.

Recent papers have demonstrated that ensemble stumps and trees could be vulnerable to small input perturbations, so robustness verification and defense for those models have become an important research problem. However, due to the structure of decision trees, where each node makes decision purely based on one feature value, all the previous works only consider the $\ell_\infty$ norm perturbation. To study robustness with respect to a general $\ell_p$ norm perturbation, one has to consider the correlation between perturbations on different features, which has not been handled by previous algorithms. In this paper, we study the problem of robustness verification and certified defense with respect to general $\ell_p$ norm perturbations for ensemble decision stumps and trees. For robustness verification of ensemble stumps, we prove that complete verification is NP-complete for $p\in(0, \infty)$ while polynomial time algorithms exist for $p=0$ or $\infty$. For $p\in(0, \infty)$ we develop an efficient dynamic programming based algorithm for sound verification of ensemble stumps. For ensemble trees, we generalize the previous multi-level robustness verification algorithm to $\ell_p$ norm. We demonstrate the first certified defense method for training ensemble stumps and trees with respect to $\ell_p$ norm perturbations, and verify its effectiveness empirically on real datasets.

We take a more rigorous look at Relativistic Generative Adversarial Networks (RGANs) and prove that the objective function of the discriminator is a statistical divergence for any concave function $f$ with minimal properties ($f(0)=0$, $f'(0) \neq 0$, $\sup_x f(x)>0$). We devise additional variants of relativistic $f$-divergences. We show that the Wasserstein distance is weaker than $f$-divergences which are weaker than relativistic $f$-divergences. Given the good performance of RGANs, this suggests that Wasserstein GAN does not performs well primarily because of the weak metric, but rather because of regularization and the use of a relativistic discriminator. We introduce the minimum-variance unbiased estimator (MVUE) for Relativistic paired GANs (RpGANs; originally called RGANs which could bring confusion) and show that it does not perform better. We show that the estimator of Relativistic average GANs (RaGANs) is asymptotically unbiased and that the finite-sample bias is small; removing this bias does not improve performance.

We revisit the optimization from samples (OPS) model, which studies the problem of optimizing objective functions directly from the sample data. Previous results showed that we cannot obtain a constant approximation ratio for the maximum coverage problem using polynomially many independent samples of the form $\{S_i, f(S_i)\}_{i=1}^t$ (Balkanski et al., 2017), even if coverage functions are $(1 - \epsilon)$-PMAC learnable using these samples (Badanidiyuru et al., 2012), which means most of the function values can be approximately learned very well with high probability. In this work, to circumvent the impossibility result of OPS, we propose a stronger model called optimization from structured samples (OPSS) for coverage functions, where the data samples encode the structural information of the functions. We show that under three general assumptions on the sample distributions, we can design efficient OPSS algorithms that achieve a constant approximation for the maximum coverage problem. We further prove a constant lower bound under these assumptions, which is tight when not considering computational efficiency. Moreover, we also show that if we remove any one of the three assumptions, OPSS for the maximum coverage problem has no constant approximation.

For distributions $\mathbb{P}$ and $\mathbb{Q}$ with different supports or undefined densities, the divergence $\textrm{D}(\mathbb{P}||\mathbb{Q})$ may not exist. We define a Spread Divergence $\tilde{\textrm{D}}(\mathbb{P}||\mathbb{Q})$ on modified $\mathbb{P}$ and $\mathbb{Q}$ and describe sufficient conditions for the existence of such a divergence. We demonstrate how to maximize the discriminatory power of a given divergence by parameterizing and learning the spread. We also give examples of using a Spread Divergence to train implicit generative models, including linear models (Independent Components Analysis) and non-linear models (Deep Generative Networks).