AISTATS 2022 Papers

In this work, we study policy-based methods for solving the reinforcement learning problem, where off-policy sampling and linear function approximation are employed for policy evaluation, and various policy update rules (including natural policy gradient) are considered for policy improvement. To solve the policy evaluation sub-problem in the presence of the deadly triad, we propose a generic algorithm framework of multi-step TD-learning with generalized importance sampling ratios, which includes two specific algorithms: the $\lambda$-averaged $Q$-trace and the two-sided $Q$-trace. The generic algorithm is single time-scale, has provable finite-sample guarantees, and overcomes the high variance issue in off-policy learning. As for the policy improvement, we provide a universal analysis that establishes geometric convergence of various policy update rules, which leads to an overall $\Tilde{\mathcal{O}}(\epsilon^{-2})$ sample complexity.

Motivated by practical needs in online experimentation and off-policy learning, we study the problem of safe optimal design, where we develop a data logging policy that efficiently explores while achieving competitive rewards with a baseline production policy. We first show, perhaps surprisingly, that a common practice of mixing the production policy with uniform exploration, despite being safe, is sub-optimal in maximizing information gain. Then we propose a safe optimal logging policy for the case when no side information about the actions’ expected rewards is available. We improve upon this design by considering side information and also extend both approaches to a large number of actions with a linear reward model. We analyze how our data logging policies impact errors in off-policy learning. Finally, we empirically validate the benefit of our designs by conducting extensive experiments.

Multi-output regression problems are commonly encountered in science and engineering. In particular, multi-output Gaussian processes have been emerged as a promising tool for modeling these complex systems since they can exploit the inherent correlations and provide reliable uncertainty estimates. In many applications, however, acquiring the data is expensive and safety concerns might arise (e.g. robotics, engineering). We propose a safe active learning approach for multi-output Gaussian process regression. This approach queries the most informative data or output taking the relatedness between the regressors and safety constraints into account. We prove the effectiveness of our approach by providing theoretical analysis and by demonstrating empirical results on simulated datasets and on a real-world engineering dataset. On all datasets, our approach shows improved convergence compared to its competitors.

Interpretability of learning algorithms is crucial for applications involving critical decisions, and variable importance is one of the main interpretation tools. Shapley effects are now widely used to interpret both tree ensembles and neural networks, as they can efficiently handle dependence and interactions in the data, as opposed to most other variable importance measures. However, estimating Shapley effects is a challenging task, because of the computational complexity and the conditional expectation estimates. Accordingly, existing Shapley algorithms have flaws: a costly running time, or a bias when input variables are dependent. Therefore, we introduce SHAFF, SHApley eFfects via random Forests, a fast and accurate Shapley effect estimate, even when input variables are dependent. We show SHAFF efficiency through both a theoretical analysis of its consistency, and the practical performance improvements over competitors with extensive experiments. An implementation of SHAFF in C++ and R is available online.

We present a principled approach for designing stochastic Newton methods for solving finite sum optimization problems. Our approach has two steps. First, we re-write the stationarity conditions as a system of nonlinear equations that associates each data point to a new row. Second, we apply a Subsampled Newton Raphson method to solve this system of nonlinear equations. Using our approach, we develop a new Stochastic Average Newton (SAN) method, which is incremental by design, in that it requires only a single data point per iteration. It is also cheap to implement when solving regularized generalized linear models, with a cost per iteration of the order of the number of the parameters. We show through extensive numerical experiments that SAN requires no knowledge about the problem, neither parameter tuning, while remaining competitive as compared to classical variance reduced gradient methods (e.g. SAG and SVRG), incremental Newton and quasi-Newton methods (e.g. SNM, IQN).

Labelling of data for supervised learning can be costly and time-consuming and the risk of incorporating label noise in large data sets is imminent. When training a flexible discriminative model using a strictly proper loss, such noise will inevitably shift the solution towards the conditional distribution over noisy labels. Nevertheless, while deep neural networks have proven capable of fitting random labels, regularisation and the use of robust loss functions empirically mitigate the effects of label noise. However, such observations concern robustness in accuracy, which is insufficient if reliable uncertainty quantification is critical. We demonstrate this by analysing the properties of the conditional distribution over noisy labels for an input-dependent noise model. In addition, we evaluate the set of robust loss functions characterised by noise-insensitive, asymptotic risk minimisers. We find that strictly proper and robust loss functions both offer asymptotic robustness in accuracy, but neither guarantee that the final model is calibrated. Moreover, even with robust loss functions, overfitting is an issue in practice. With these results, we aim to explain observed robustness of common training practices, such as early stopping, to label noise. In addition, we aim to encourage the development of new noise-robust algorithms that not only preserve accuracy but that also ensure reliability.

Geometric median (GM) is a classical method in statistics for achieving robust estimation of the uncorrupted data; under gross corruption, it achieves the optimal breakdown point of 1/2. However, its computational complexity makes it infeasible for robustifying stochastic gradient descent (SGD) in high-dimensional optimization problems. In this paper, we show that by applying GM to only a judiciously chosen block of coordinates at a time and using a memory mechanism, one can retain the breakdown point of 1/2 for smooth non-convex problems, with non-asymptotic convergence rates comparable to the SGD with GM while resulting in significant speedup in training. We further validate the run-time and robustness of our approach empirically on several popular deep learning tasks. Code available at: https://github.com/anishacharya/BGMD

Stochastic linear contextual bandit algorithms have substantial applications in practice, such as recommender systems, online advertising, clinical trials, etc. Recent works show that optimal bandit algorithms are vulnerable to adversarial attacks and can fail completely in the presence of attacks. Existing robust bandit algorithms only work for the non-contextual setting under the attack of rewards and cannot improve the robustness in the general and popular contextual bandit environment. In addition, none of the existing methods can defend against attacked context. In this work, we provide the first robust bandit algorithm for stochastic linear contextual bandit setting under a fully adaptive and omniscient attack with sub-linear regret. Our algorithm not only works under the attack of rewards, but also under attacked context. Moreover, it does not need any information about the attack budget or the particular form of the attack. We provide theoretical guarantees for our proposed algorithm and show by experiments that our proposed algorithm improves the robustness against various kinds of popular attacks.

Probabilistic time series forecasting has played critical role in decision-making processes due to its capability to quantify uncertainties. Deep forecasting models, however, could be prone to input perturbations, and the notion of such perturbations, together with that of robustness, has not even been completely established in the regime of probabilistic forecasting. In this work, we propose a framework for robust probabilistic time series forecasting. First, we generalize the concept of adversarial input perturbations, based on which we formulate the concept of robustness in terms of bounded Wasserstein deviation. Then we extend the randomized smoothing technique to attain robust probabilistic forecasters with theoretical robustness certificates against certain classes of adversarial perturbations. Lastly, extensive experiments demonstrate that our methods are empirically effective in enhancing the forecast quality under additive adversarial attacks and forecast consistency under supplement of noisy observations. The code for our experiments is available at https://github.com/tetrzim/robust-probabilistic-forecasting.

Crowdsourcing systems enable us to collect large-scale dataset, but inherently suffer from noisy labels of low-paid workers. We address the inference and learning problems using such a crowdsourced dataset with noise. Due to the nature of sparsity in crowdsourcing, it is critical to exploit both probabilistic model to capture worker prior and neural network to extract task feature despite risks from wrong prior and overfitted feature in practice. We hence establish a neural-powered Bayesian framework, from which we devise deepMF and deepBP with different choice of variational approximation methods, mean field (MF) and belief propagation (BP), respectively. This provides a unified view of existing methods, which are special cases of deepMF with different priors. In addition, our empirical study suggests that deepBP is a new approach, which is more robust against wrong prior, feature overfitting and extreme workers thanks to the more sophisticated BP than MF.

Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in those cases. In this paper, we propose a novel algorithm based on the posterior bootstrap and maximum mean discrepancy estimators. This leads to a highly-parallelisable Bayesian inference algorithm with strong robustness properties. This is demonstrated through an in-depth theoretical study which includes generalisation bounds and proofs of frequentist consistency and robustness of our posterior. The approach is then assessed on a range of examples including a g-and-k distribution and a toggle-switch model.

In reinforcement learning, we encode the potential behaviors of an agent interacting with an environment into an infinite set of policies, called policy space, typically represented by a family of parametric functions. Dealing with such a policy space is a hefty challenge, which often causes sample and computational inefficiencies. However, we argue that a limited number of policies are actually relevant when we also account for the structure of the environment and of the policy parameterization, as many of them would induce very similar interactions, i.e., state-action distributions. In this paper, we seek for a reward-free compression of the policy space into a finite set of representative policies, such that, given any policy $\pi$, the minimum Rényi divergence between the state-action distributions of the representative policies and the state-action distribution of $\pi$ is bounded. We show that this compression of the policy space can be formulated as a set cover problem, and it is inherently NP-hard. Nonetheless, we propose a game-theoretic reformulation for which a locally optimal solution can be efficiently found by iteratively stretching the compressed space to cover the most challenging policy. Finally, we provide an empirical evaluation to illustrate the compression procedure in simple domains, and its ripple effects in reinforcement learning.

Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as Boltzmann distributions. Several procedures have been proposed to solve this problem but many of them sacrifice invertibility and, thereby, tractability of the log-likelihood as well as other desirable properties. To address these limitations, we introduce a base distribution for normalizing flows based on learned rejection sampling, allowing the resulting normalizing flow to model complicated distributions without giving up bijectivity. Furthermore, we develop suitable learning algorithms using both maximizing the log-likelihood and the optimization of the Kullback-Leibler divergence, and apply them to various sample problems, i.e. approximating 2D densities, density estimation of tabular data, image generation, and modeling Boltzmann distributions. In these experiments our method is competitive with or outperforms the baselines.

Statistical Relational Learning (SRL) models have attracted significant attention due to their ability to model complex data while handling uncertainty. However, most of these models have been restricted to discrete domains owing to the complexity of inference in continuous domains. In this work, we introduce Relational Neural Markov Random Fields (RN-MRFs) that allow handling of complex relational hybrid domains, i.e., those that include discrete and continuous quantities, and we propose a maximum pseudolikelihood estimation-based learning algorithm with importance sampling for training the neural potential parameters. The key advantage of our approach is that it makes minimal data distributional assumptions and can seamlessly embed human knowledge through potentials or relational rules. Our empirical evaluations across diverse domains, such as image processing and relational object mapping, demonstrate its practical utility.

We consider the task of generating exact samples from a target distribution, known up to normalization, over a finite alphabet. The classical algorithm for this task is rejection sampling, and although it has been used in practice for decades, there is surprisingly little study of its fundamental limitations. In this work, we study the query complexity of rejection sampling in a minimax framework for various classes of discrete distributions. Our results provide new algorithms for sampling whose complexity scales sublinearly with the alphabet size. When applied to adversarial bandits, we show that a slight modification of the EXP3 algorithm reduces the per-iteration complexity from O(K) to O(log(K) log(K/\ensuremath{\delta})) with probability 1-\ensuremath{\delta}, where K is the number of arms.

In this work, we study model-based reinforcement learning (RL) in unknown stabilizable linear dynamical systems. When learning a dynamical system, one needs to stabilize the unknown dynamics in order to avoid system blow-ups. We propose an algorithm that certifies fast stabilization of the underlying system by effectively exploring the environment with an improved exploration strategy. We show that the proposed algorithm attains $\Tilde{\mathcal{O}}(\sqrt{T})$ regret after $T$ time steps of agent-environment interaction. We also show that the regret of the proposed algorithm has only a polynomial dependence in the problem dimensions, which gives an exponential improvement over the prior methods. Our improved exploration method is simple, yet efficient, and it combines a sophisticated exploration policy in RL with an isotropic exploration strategy to achieve fast stabilization and improved regret. We empirically demonstrate that the proposed algorithm outperforms other popular methods in several adaptive control tasks.

Making an informed decision—for example, when choosing a career or housing—requires knowledge about the available options. Such knowledge is generally acquired through costly trial and error, but this learning process can be disrupted by competition. In this work, we study how competition affects the long-term outcomes of individuals as they learn. We build on a line of work that models this setting as a two-sided matching market with bandit learners. A recent result in this area states that it is impossible to simultaneously guarantee two natural desiderata: stability and low optimal regret for all agents. Resource-allocating platforms can point to this result as a justification for assigning good long-term outcomes to some agents and poor ones to others. We show that this impossibility need not hold true. In particular, by modeling two additional components of competition—namely, costs and transfers—we prove that it is possible to simultaneously guarantee four desiderata: stability, low optimal regret, fairness in the distribution of regret, and high social welfare.

The expected improvement (EI) algorithm is one of the most popular strategies for optimization under uncertainty due to its simplicity and efficiency. Despite its popularity, the theoretical aspects of this algorithm have not been properly analyzed. In particular, whether in the noisy setting, the EI strategy with a standard incumbent converges is still an open question of the Gaussian process bandit optimization problem. We aim to answer this question by proposing a variant of EI with a standard incumbent defined via the GP predictive mean. We prove that our algorithm converges, and achieves a cumulative regret bound of $\mathcal O(\gamma_T\sqrt{T})$, where $\gamma_T$ is the maximum information gain between $T$ observations and the Gaussian process model. Based on this variant of EI, we further propose an algorithm called Improved GP-EI that converges faster than previous counterparts. In particular, our proposed variants of EI do not require the knowledge of the RKHS norm and the noise’s sub-Gaussianity parameter as in previous works. Empirical validation in our paper demonstrates the effectiveness of our algorithms compared to several baselines.

We study the problem of learning tree-structured Markov random fields (MRF) on discrete random variables with common support when the observations are corrupted by a k-ary symmetric noise channel with unknown probability of error. For Ising models (support size = 2), past work has shown that graph structure can only be recovered up to the leaf clusters (a leaf node, its parent, and its siblings form a leaf cluster) and exact recovery is impossible. No prior work has addressed the setting of support size of 3 or more, and indeed this setting is far richer. As we show, when the support size is 3 or more, the structure of the leaf clusters may be partially or fully identifiable. We provide a precise characterization of this phenomenon and show that the extent of recoverability is dictated by the joint PMF of the random variables. In particular, we provide necessary and sufficient conditions for exact recoverability. Furthermore, we present a polynomial time, sample efficient algorithm that recovers the exact tree when this is possible, or up to the unidentifiability as promised by our characterization, when full recoverability is impossible. Finally, we demonstrate the efficacy of our algorithm experimentally.