Batch reinforcement learning (RL) broadly refers to the problem of finding a policy with high expected return in a stochastic control problem when only a batch of data collected from the controlled system is available. Here, we consider this problem for finite state-action ("tabular") Markov decision processes (MDPs) when the data takes the form of trajectories obtained by following some logging policy. In more details, the trajectories are composed of sequences of states, actions, and rewards, where the action is chosen by the logging policy and the next state and rewards follow the distributions specified by the MDP's transition parameters. Arguably, this is the most natural problem setting to consider in batch learning. The basic questions are (a) what logging policy should one choose to generate the data so as to maximize the chance of obtaining a good policy with as little data as possible; and (b) how many transitions are sufficient and necessary to obtain a good policy and which algorithm to use to obtain such a policy? Note that here the logging policy needs to be chosen a priori, that is, before the data collection process begins. An alternative way of saying this is that the data collection is done in a passive way. Our main results are as follows: First, we show that (perhaps unsurprisingly), in the lack of extra information about the nature of the MDP, the best logging policy should choose actions uniformly at random. Next, we show that the number of transitions necessary and sufficient to obtain a good policy, the sample complexity of learning, is an exponential function of the minimum of the number of states and the planning horizon.

Recent renewed interest in multi-agent reinforcement learning (MARL) has generated an impressive array of techniques that leverage deep reinforcement learning, primarily actor-critic architectures, and can be applied to a limited range of settings in terms of observability and communication. However, a continuing limitation of much of this work is the curse of dimensionality when it comes to representations based on joint actions, which grow exponentially with the number of agents. In this paper, we squarely focus on this challenge of scalability. We apply the key insight of action anonymity, which leads to permutation invariance of joint actions, to two recently presented deep MARL algorithms, MADDPG and IA2C, and compare these instantiations to another recent technique that leverages action anonymity, viz., mean-field MARL. We show that our instantiations can learn the optimal behavior in a broader class of agent networks than the mean-field method, using a recently introduced pragmatic domain.

We introduce a new general identifiable framework for principled disentanglement referred to as Structured Nonlinear Independent Component Analysis (SNICA). Our contribution is to extend the identifiability theory of deep generative models for a very broad class of structured models. While previous works have shown identifiability for specific classes of time-series models, our theorems extend this to more general temporal structures as well as to models with more complex structures such as spatial dependencies. In particular, we establish the major result that identifiability for this framework holds even in the presence of noise of unknown distribution. The SNICA setting therefore subsumes all the existing nonlinear ICA models for time-series and also allows for new much richer identifiable models. Finally, as an example of our framework's flexibility, we introduce the first nonlinear ICA model for time-series that combines the following very useful properties: it accounts for both nonstationarity and autocorrelation in a fully unsupervised setting; performs dimensionality reduction; models hidden states; and enables principled estimation and inference by variational maximum-likelihood.

This work has been submitted to the IEEE for possible publication. Abstract With the development of the 5G and Internet of Things, amounts of wireless devices need to share the limited spectrum resources. Dynamic spectrum access (DSA) is a promising paradigm to remedy the problem of inef!cient spectrum utilization brought upon by the historical command-and-control approach to spectrum allocation. In this paper, we investigate the distributed DSA problem for multiuser in a typical multi-channel cognitive radio network. The problem is formulated as a decentralized partially observable Markov decision process (Dec-POMDP), and we proposed a centralized off-line training and distributed on-line execution framework based on cooperative multi-agent reinforcement learning (MARL). We employ the deep recurrent Q-network (DRQN) to address the partial observability of the state for each cognitive user. The ultimate goal is to learn a cooperative strategy which maximizes the sum throughput of cognitive radio network in distributed fashion without coordination information exchange between cognitive users. This work was supported in part by the National Natural Science Foundation of China under Grant 6193000305. X. Tan, L. Zhou, Y. Sun, H. Wang, H. Zhao and J. Wei are all with College of Electronic Science and Technology, National University of Defense Technology, Changsha, 410073, China (E-mail: {tanxiang, zhouli2035, haijunwang14, sunyuli19, haitaozhao, wjbhw}@nudt.edu.cn). Boon-Chong Seet is with the Department of Electrical and Electronic Engineering, Auckland University of Technology, Auckland 1142, New Zealand (E-mail: boon-chong.seet@aut.ac.nz). Victor C. M. Leung is with Shenzhen University, Shenzhen, China and the University of British Columbia, Vancouver, Canada (E-mail: vleung@ieee.org). 2 From the simulation results, we can observe that the proposed algorithm can converge fast and achieve almost the optimal performance. The future network is involving into the Internet of Everything.

In many real-world imitation learning tasks, the demonstrator and the learner have to act in different but full observation spaces. This situation generates significant obstacles for existing imitation learning approaches to work, even when they are combined with traditional space adaptation techniques. The main challenge lies in bridging expert's occupancy measures to learner's dynamically changing occupancy measures under the different observation spaces. In this work, we model the above learning problem as Heterogeneous Observations Imitation Learning (HOIL). We propose the Importance Weighting with REjection (IWRE) algorithm based on the techniques of importance-weighting, learning with rejection, and active querying to solve the key challenge of occupancy measure matching. Experimental results show that IWRE can successfully solve HOIL tasks, including the challenging task of transforming the vision-based demonstrations to random access memory (RAM)-based policies under the Atari domain.

To understand the behavior of large dynamical systems like transportation networks, one must often rely on measurements transmitted by a set of sensors, for instance individual vehicles. Such measurements are likely to be incomplete and imprecise, which makes it hard to recover the underlying signal of interest.Hoping to quantify this phenomenon, we study the properties of a partially-observed state-space model. In our setting, the latent state $X$ follows a high-dimensional Vector AutoRegressive process $X_t = \theta X_{t-1} + \varepsilon_t$. Meanwhile, the observations $Y$ are given by a noise-corrupted random sample from the state $Y_t = \Pi_t X_t + \eta_t$. Several random sampling mechanisms are studied, allowing us to investigate the effect of spatial and temporal correlations in the distribution of the sampling matrices $\Pi_t$.We first prove a lower bound on the minimax estimation error for the transition matrix $\theta$. We then describe a sparse estimator based on the Dantzig selector and upper bound its non-asymptotic error, showing that it achieves the optimal convergence rate for most of our sampling mechanisms. Numerical experiments on simulated time series validate our theoretical findings, while an application to open railway data highlights the relevance of this model for public transport traffic analysis.

Pretrained language models have achieved state-of-the-art performance when adapted to a downstream NLP task. However, theoretical analysis of these models is scarce and challenging since the pretraining and downstream tasks can be very different. We propose an analysis framework that links the pretraining and downstream tasks with an underlying latent variable generative model of text -- the downstream classifier must recover a function of the posterior distribution over the latent variables. We analyze head tuning (learning a classifier on top of the frozen pretrained model) and prompt tuning in this setting. The generative model in our analysis is either a Hidden Markov Model (HMM) or an HMM augmented with a latent memory component, motivated by long-term dependencies in natural language. We show that 1) under certain non-degeneracy conditions on the HMM, simple classification heads can solve the downstream task, 2) prompt tuning obtains downstream guarantees with weaker non-degeneracy conditions, and 3) our recovery guarantees for the memory-augmented HMM are stronger than for the vanilla HMM because task-relevant information is easier to recover from the long-term memory. Experiments on synthetically generated data from HMMs back our theoretical findings.

Search is an important tool for computing effective policies in single- and multi-agent environments, and has been crucial for achieving superhuman performance in several benchmark fully and partially observable games. However, one major limitation of prior search approaches for partially observable environments is that the computational cost scales poorly with the amount of hidden information. In this paper we present \emph{Learned Belief Search} (LBS), a computationally efficient search procedure for partially observable environments. Rather than maintaining an exact belief distribution, LBS uses an approximate auto-regressive counterfactual belief that is learned as a supervised task. In multi-agent settings, LBS uses a novel public-private model architecture for underlying policies in order to efficiently evaluate these policies during rollouts. In the benchmark domain of Hanabi, LBS can obtain 55% ~ 91% of the benefit of exact search while reducing compute requirements by $35.8 \times$ ~ $4.6 \times$, allowing it to scale to larger settings that were inaccessible to previous search methods.

With the advent of direct models in automatic speech recognition (ASR), the formerly prevalent frame-wise acoustic modeling based on hidden Markov models (HMM) diversified into a number of modeling architectures like encoder-decoder attention models, transducer models and segmental models (direct HMM). While transducer models stay with a frame-level model definition, segmental models are defined on the level of label segments directly. While (soft-)attention-based models avoid explicit alignment, transducer and segmental approach internally do model alignment, either by segment hypotheses or, more implicitly, by emitting so-called blank symbols. In this work, we prove that the widely used class of RNN-Transducer models and segmental models (direct HMM) are equivalent and therefore show equal modeling power. It is shown that blank probabilities translate into segment length probabilities and vice versa. In addition, we provide initial experiments investigating decoding and beam-pruning, comparing time-synchronous and label-/segment-synchronous search strategies and their properties using the same underlying model.

In real-world multi-agent systems, agents with different capabilities may join or leave without altering the team's overarching goals. Coordinating teams with such dynamic composition is challenging: the optimal team strategy varies with the composition. We propose COPA, a coach-player framework to tackle this problem. We assume the coach has a global view of the environment and coordinates the players, who only have partial views, by distributing individual strategies. Specifically, we 1) adopt the attention mechanism for both the coach and the players; 2) propose a variational objective to regularize learning; and 3) design an adaptive communication method to let the coach decide when to communicate with the players. We validate our methods on a resource collection task, a rescue game, and the StarCraft micromanagement tasks. We demonstrate zero-shot generalization to new team compositions. Our method achieves comparable or better performance than the setting where all players have a full view of the environment. Moreover, we see that the performance remains high even when the coach communicates as little as 13% of the time using the adaptive communication strategy.