There are great interests as well as many challenges in applying reinforcement learning (RL) to recommendation systems. In this setting, an online user is the environment; neither the reward function nor the environment dynamics are clearly defined, making the application of RL challenging. In this paper, we propose a novel model-based reinforcement learning framework for recommendation systems, where we develop a generative adversarial network to imitate user behavior dynamics and learn her reward function. Using this user model as the simulation environment, we develop a novel DQN algorithm to obtain a combinatorial recommendation policy which can handle a large number of candidate items efficiently. In our experiments with real data, we show this generative adversarial user model can better explain user behavior than alternatives, and the RL policy based on this model can lead to a better long-term reward for the user and higher click rate for the system.

This paper studies the dynamic generator model for spatial-temporal processes such as dynamic textures and action sequences in video data. In this model, each time frame of the video sequence is generated by a generator model, which is a non-linear transformation of a latent state vector, where the non-linear transformation is parametrized by a top-down neural network. The sequence of latent state vectors follows a non-linear auto-regressive model, where the state vector of the next frame is a non-linear transformation of the state vector of the current frame as well as an independent noise vector that provides randomness in the transition. The non-linear transformation of this transition model can be parametrized by a feedforward neural network. We show that this model can be learned by an alternating back-propagation through time algorithm that iteratively samples the noise vectors and updates the parameters in the transition model and the generator model. We show that our training method can learn realistic models for dynamic textures and action patterns.

We propose a general formulation for addressing reinforcement learning (RL) problems in settings with observational data. That is, we consider the problem of learning good policies solely from historical data in which unobserved factors (confounders) affect both observed actions and rewards. Our formulation allows us to extend a representative RL algorithm, the Actor-Critic method, to its deconfounding variant, with the methodology for this extension being easily applied to other RL algorithms. In addition to this, we develop a new benchmark for evaluating deconfounding RL algorithms by modifying the OpenAI Gym environments and the MNIST dataset. Using this benchmark, we demonstrate that the proposed algorithms are superior to traditional RL methods in confounded environments with observational data. To the best of our knowledge, this is the first time that confounders are taken into consideration for addressing full RL problems with observational data. Code is available at https://github.com/CausalRL/DRL.

The rising volume of datasets has made training machine learning (ML) models a major computational cost in the enterprise. Given the iterative nature of model and parameter tuning, many analysts use a small sample of their entire data during their initial stage of analysis to make quick decisions (e.g., what features or hyperparameters to use) and use the entire dataset only in later stages (i.e., when they have converged to a specific model). This sampling, however, is performed in an ad-hoc fashion. Most practitioners cannot precisely capture the effect of sampling on the quality of their model, and eventually on their decision-making process during the tuning phase. Moreover, without systematic support for sampling operators, many optimizations and reuse opportunities are lost. In this paper, we introduce BlinkML, a system for fast, quality-guaranteed ML training. BlinkML allows users to make error-computation tradeoffs: instead of training a model on their full data (i.e., full model), BlinkML can quickly train an approximate model with quality guarantees using a sample. The quality guarantees ensure that, with high probability, the approximate model makes the same predictions as the full model. BlinkML currently supports any ML model that relies on maximum likelihood estimation (MLE), which includes Generalized Linear Models (e.g., linear regression, logistic regression, max entropy classifier, Poisson regression) as well as PPCA (Probabilistic Principal Component Analysis). Our experiments show that BlinkML can speed up the training of large-scale ML tasks by 6.26x-629x while guaranteeing the same predictions, with 95% probability, as the full model.

A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. The score matching method of Hyv\"arinen [2005] avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over $\mathbb{R}^m$. Hyv\"arinen [2007] extended the approach to distributions supported on the non-negative orthant, $\mathbb{R}_+^m$. In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. As an example, we consider a general class of pairwise interaction models. Addressing an overlooked inexistence problem, we generalize the regularized score matching method of Lin et al. [2016] and improve its theoretical guarantees for non-negative Gaussian graphical models.

A central machine is interested in estimating the underlying structure of a sparse Gaussian Graphical Model (GGM) from datasets distributed across multiple local machines. The local machines can communicate with the central machine through a wireless multiple access channel. In this paper, we are interested in designing effective strategies where reliable learning is feasible under power and bandwidth limitations. Two approaches are proposed: Signs and Uncoded methods. In Signs method, the local machines quantize their data into binary vectors and an optimal channel coding scheme is used to reliably send the vectors to the central machine where the structure is learned from the received data. In Uncoded method, data symbols are scaled and transmitted through the channel. The central machine uses the received noisy symbols to recover the structure. Theoretical results show that both methods can recover the structure with high probability for large enough sample size. Experimental results indicate the superiority of Signs method over Uncoded method under several circumstances.

Abstract--In this paper, reinforcement learning is applied to the problem of optimizing market making. A multi-agent reinforcement learning framework is used to optimally place limit orders that lead to successful trades. The framework consists of two agents. The macro-agent optimizes on making the decision to buy, sell, or hold an asset. For the context of this paper, the proposed framework is applied and studied on the Bitcoin cryptocurrency market. The goal of this paper is to show that reinforcement learning is a viable strategy that can be applied to complex problems (with complex environments) such as market making. Algorithmic trading, and in particular high-frequency algorithmic trading (HFT), has gained immense popularity in the recent decade. With advances in hardware and software, algorithmic trading has rapidly become the norm. The increasing popularity of machine learning has slowly made its way to financial markets [1], where it is primarily used to predict price movements of assets. However, there are a number of challenges that these classic machine learning techniques entail: 1) Prediction time: In machine learning, model complexity can have an impact on prediction time. Many times, in the supervised learning setting, neural networks are used to make predictions. Due to the computational complexity that comes with these models, as the model complexity increases, the decision time also increases [2]. In the HFT setting, by the time the model makes a prediction, it may already be too late to take the predicted action. The problem then becomes, how can these added latency costs be incorporated into our prediction? The general rule of thumb in finance is that the historical performance of an asset does not predict the future performance of the asset, i.e. forecasting and predicting the market from historical performance alone is virtually impossible.

We address the problem of two-variable causal inference. This task is to infer an existing causal relation between two random variables, i.e. $X \rightarrow Y$ or $Y \rightarrow X$, from purely observational data. We briefly review a number of state-of-the-art methods for this, including very recent ones. A novel inference method is introduced, Bayesian Causal Inference (BCI), which assumes a generative Bayesian hierarchical model to pursue the strategy of Bayesian model selection. In the model the distribution of the cause variable is given by a Poisson lognormal distribution, which allows to explicitly regard discretization effects. We assume Fourier diagonal Field covariance operators. The generative model assumed provides synthetic causal data for benchmarking our model in comparison to existing State-of-the-art models, namely LiNGAM, ANM-HSIC, ANM-MML, IGCI and CGNN. We explore how well the above methods perform in case of high noise settings, strongly discretized data and very sparse data. BCI performs generally reliable with synthetic data as well as with the real world TCEP benchmark set, with an accuracy comparable to state-of-the-art algorithms.

The Normal Means problem plays a fundamental role in many areas of modern high-dimensional statistics, both in theory and practice. And the Empirical Bayes (EB) approach to solving this problem has been shown to be highly effective, again both in theory and practice. However, almost all EB treatments of the Normal Means problem assume that the observations are independent. In practice correlations are ubiquitous in real-world applications, and these correlations can grossly distort EB estimates. Here, exploiting theory from Schwartzman (2010), we develop new EB methods for solving the Normal Means problem that take account of unknown correlations among observations. We provide practical software implementations of these methods, and illustrate them in the context of large-scale multiple testing problems and False Discovery Rate (FDR) control. In realistic numerical experiments our methods compare favorably with other commonly-used multiple testing methods.

In this paper, we develop a new approach to learning high-dimensional Poisson directed acyclic graphical (DAG) models from only observational data without strong assumptions such as faithfulness and strong sparsity. A key component of our method is to decouple the ordering estimation or parent search where the problems can be efficiently addressed using $\ell_1$-regularized regression and the mean-variance relationship. We show that sample size $n = \Omega( d^{2} \log^{9} p)$ is sufficient for our polynomial time Mean-variance Ratio Scoring (MRS) algorithm to recover the true directed graph, where $p$ is the number of nodes and $d$ is the maximum indegree. We verify through simulations that our algorithm is statistically consistent in the high-dimensional $p>n$ setting, and performs well compared to state-of-the-art ODS, GES, and MMHC algorithms. We also demonstrate through multivariate real count data that our MRS algorithm is well-suited to estimating DAG models for multivariate count data in comparison to other methods used for discrete data.