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Reinforcement Learning of Simple Indirect Mechanisms

arXiv.org Artificial Intelligence

Over the last fifty years, a large body of research in microeconomics has introduced many different mechanisms for resource allocation. Despite the wide variety of available options, "simple" mechanisms such as posted price and serial dictatorship are often preferred for practical applications, including housing allocation [AbdulkadiroฤŸlu and Sรถnmez, 1998], online procurement [Badanidiyuru et al., 2012], or allocation of medical appointments [Klaus and Nichifor, 2019]. There has been considerable interest in formalizing different notions of simplicity. Li [2017] identifies mechanisms that are particularly simple from a strategic perspective, introducing the concept of obviously strategyproof mechanisms; under obviously strategyproof mechanisms, it is obvious that an agent cannot profit by trying to game the system, as even the worst possible final outcome from behaving truthfully is at least as good as the best possible outcome from any other strategy. Pycia and Troyan [2019] introduce the still stronger concept of strongly obviously strategyproof (SOSP) mechanisms, and show that this class can essentially be identified with sequential price mechanisms, where agents are visited in turn and offered a choice from a menu of options (which may or may not include transfers). SOSP mechanisms are ones in which an agent is not even required to consider her future (truthful) actions to understand that the mechanism is obviously strategyproof.


Exploration in Approximate Hyper-State Space for Meta Reinforcement Learning

arXiv.org Artificial Intelligence

Meta-learning is a powerful tool for learning policies that can adapt efficiently when deployed in new tasks. If however the meta-training tasks have sparse rewards, the need for exploration during meta-training is exacerbated given that the agent has to explore and learn across many tasks. We show that current meta-learning methods can fail catastrophically in such environments. To address this problem, we propose HyperX, a novel method for meta-learning in sparse reward tasks. Using novel reward bonuses for meta-training, we incentivise the agent to explore in approximate hyper-state space, i.e., the joint state and approximate belief space, where the beliefs are over tasks. We show empirically that these bonuses allow an agent to successfully learn to solve sparse reward tasks where existing meta-learning methods fail.


VAEBM: A Symbiosis between Variational Autoencoders and Energy-based Models

arXiv.org Machine Learning

Energy-based models (EBMs) have recently been successful in representing complex distributions of small images. However, sampling from them requires expensive Markov chain Monte Carlo (MCMC) iterations that mix slowly in high dimensional pixel space. Unlike EBMs, variational autoencoders (VAEs) generate samples quickly and are equipped with a latent space that enables fast traversal of the data manifold. However, VAEs tend to assign high probability density to regions in data space outside the actual data distribution and often fail at generating sharp images. In this paper, we propose VAEBM, a symbiotic composition of a VAE and an EBM that offers the best of both worlds. VAEBM captures the overall mode structure of the data distribution using a state-of-the-art VAE and it relies on its EBM component to explicitly exclude non-data-like regions from the model and refine the image samples. Moreover, the VAE component in VAEBM allows us to speed up MCMC updates by reparameterizing them in the VAE's latent space. Our experimental results show that VAEBM outperforms state-of-the-art VAEs and EBMs in generative quality on several benchmark image datasets by a large margin. It can generate high-quality images as large as 256$\times$256 pixels with short MCMC chains. We also demonstrate that VAEBM provides complete mode coverage and performs well in out-of-distribution detection.


Minimax Optimal Reinforcement Learning for Discounted MDPs

arXiv.org Machine Learning

The goal of reinforcement learning is designing algorithms to learn the optimal policy through interactions with the unknown dynamic environment. Markov decision processes (MDPs) plays a central role in reinforcement learning due to their ability to describe the time-independent state transition property. In specific, the discounted MDP is one of the standard MDPs in reinforcement learning to describe sequential tasks without interruption or restart. Various reinforcement learning algorithms have been proposed for discounted MDPs. In specific, Azar et al. (2013) proposed an Empirical QVI algorithm which achieves the optimal sample complexity to find the optimal value function. Sidford et al. (2018a) proposed a sublinear randomized value iteration algorithm that achieves a near-optimal sample complexity to find the optimal policy, and Sidford et al. (2018b) further improved it to reach the optimal sample complexity.


Bayesian Policy Search for Stochastic Domains

arXiv.org Machine Learning

AI planning can be cast as inference in probabilistic models, and probabilistic programming was shown to be capable of policy search in partially observable domains. Prior work introduces policy search through Markov chain Monte Carlo in deterministic domains, as well as adapts black-box variational inference to stochastic domains, however not in the strictly Bayesian sense. In this work, we cast policy search in stochastic domains as a Bayesian inference problem and provide a scheme for encoding such problems as nested probabilistic programs. We argue that probabilistic programs for policy search in stochastic domains should involve nested conditioning, and provide an adaption of Lightweight Metropolis-Hastings (LMH) for robust inference in such programs. We apply the proposed scheme to stochastic domains and show that policies of similar quality are learned, despite a simpler and more general inference algorithm. We believe that the proposed variant of LMH is novel and applicable to a wider class of probabilistic programs with nested conditioning.


Deep learning for time series classification

arXiv.org Artificial Intelligence

Time series analysis is a field of data science which is interested in analyzing sequences of numerical values ordered in time. Time series are particularly interesting because they allow us to visualize and understand the evolution of a process over time. Their analysis can reveal trends, relationships and similarities across the data. There exists numerous fields containing data in the form of time series: health care (electrocardiogram, blood sugar, etc.), activity recognition, remote sensing, finance (stock market price), industry (sensors), etc. Time series classification consists of constructing algorithms dedicated to automatically label time series data. The sequential aspect of time series data requires the development of algorithms that are able to harness this temporal property, thus making the existing off-the-shelf machine learning models for traditional tabular data suboptimal for solving the underlying task. In this context, deep learning has emerged in recent years as one of the most effective methods for tackling the supervised classification task, particularly in the field of computer vision. The main objective of this thesis was to study and develop deep neural networks specifically constructed for the classification of time series data. We thus carried out the first large scale experimental study allowing us to compare the existing deep methods and to position them compared other non-deep learning based state-of-the-art methods. Subsequently, we made numerous contributions in this area, notably in the context of transfer learning, data augmentation, ensembling and adversarial attacks. Finally, we have also proposed a novel architecture, based on the famous Inception network (Google), which ranks among the most efficient to date.


Python Data Science with Pandas: Master 12 Advanced Projects

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Adaptive Online Estimation of Piecewise Polynomial Trends

arXiv.org Machine Learning

We consider the framework of non-stationary stochastic optimization [Besbes et al, 2015] with squared error losses and noisy gradient feedback where the dynamic regret of an online learner against a time varying comparator sequence is studied. Motivated from the theory of non-parametric regression, we introduce a new variational constraint that enforces the comparator sequence to belong to a discrete $k^{th}$ order Total Variation ball of radius $C_n$. This variational constraint models comparators that have piece-wise polynomial structure which has many relevant practical applications [Tibshirani, 2014]. By establishing connections to the theory of wavelet based non-parametric regression, we design a polynomial time algorithm that achieves the nearly optimal dynamic regret of $\tilde{O}(n^{\frac{1}{2k+3}}C_n^{\frac{2}{2k+3}})$. The proposed policy is adaptive to the unknown radius $C_n$. Further, we show that the same policy is minimax optimal for several other non-parametric families of interest.


Efficient sampling from the Bingham distribution

arXiv.org Machine Learning

The algorithm is based on rejection sampling, where the proposal distribution is a polynomial approximation of the pdf, and can be sampled from by explicitly evaluating integrals of polynomials over the sphere. Our algorithm gives exact samples, assuming exact computation of an inverse function of a polynomial. This is in contrast with Markov Chain Monte Carlo algorithms, which are not known to enjoy rapid mixing on this problem, and only give approximate samples. As a direct application, we use this to sample from the posterior distribution of a rank-1 matrix inference problem in polynomial time.


Projected Latent Markov Chain Monte Carlo: Conditional Sampling of Normalizing Flows

arXiv.org Machine Learning

We introduce Projected Latent Markov Chain Monte Carlo (PL-MCMC), a technique for sampling from the high-dimensional conditional distributions learned by a normalizing flow. We prove that a Metropolis-Hastings implementation of PL-MCMC asymptotically samples from the exact conditional distributions associated with a normalizing flow. As a conditional sampling method, PL-MCMC enables Monte Carlo Expectation Maximization (MC-EM) training of normalizing flows from incomplete data. Through experimental tests applying normalizing flows to missing data tasks for a variety of data sets, we demonstrate the efficacy of PL-MCMC for conditional sampling from normalizing flows. Conditional sampling from modeled joint probability distributions offers a statistical framework for approaching tasks involving missing and incomplete data. Deep generative models have demonstrated an exceptional capability for approximating the distributions governing complex data. Brief analysis illustrates a fundamental guarantee for generative models: the inaccuracy (i.e. Quite often, otherwise well trained generative models possess a capability for conditional inference that is regrettably locked away from our access. Normalizing flow architectures like RealNVP (Dinh et al., 2014) and GLOW (Kingma & Dhariwal, 2018) have demonstrated accurate and expressive generative performance and showing great promise for application to missing data tasks. Additionally, by enabling the calculation of exact likelihoods, normalizing flows offer convenient mathematical properties for approaching exact conditional sampling. We are therefore motivated to develop techniques for sampling from the exact conditional distributions known by normalizing flows. In this paper, we propose Projected Latent Markov Chain Monte Carlo (PL-MCMC), a conditional sampling technique that takes advantage of the convenient mathematical structure of normalizing flows by defining a Markov Chain within a flow's latent space and accepting proposed transitions based on the likelihood of the resulting imputation.