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.

Reinforcement learning is a framework for interactive decision-making with incentives sequentially revealed across time without a system dynamics model. Due to its scaling to continuous spaces, we focus on policy search where one iteratively improves a parameterized policy with stochastic policy gradient (PG) updates. In tabular Markov Decision Problems (MDPs), under persistent exploration and suitable parameterization, global optimality may be obtained. By contrast, in continuous space, the non-convexity poses a pathological challenge as evidenced by existing convergence results being mostly limited to stationarity or arbitrary local extrema. To close this gap, we step towards persistent exploration in continuous space through policy parameterizations defined by distributions of heavier tails defined by tail-index parameter alpha, which increases the likelihood of jumping in state space. Doing so invalidates smoothness conditions of the score function common to PG. Thus, we establish how the convergence rate to stationarity depends on the policy's tail index alpha, a Holder continuity parameter, integrability conditions, and an exploration tolerance parameter introduced here for the first time. Further, we characterize the dependence of the set of local maxima on the tail index through an exit and transition time analysis of a suitably defined Markov chain, identifying that policies associated with Levy Processes of a heavier tail converge to wider peaks. This phenomenon yields improved stability to perturbations in supervised learning, which we corroborate also manifests in improved performance of policy search, especially when myopic and farsighted incentives are misaligned.

While multitask representation learning has become a popular approach in reinforcement learning (RL), theoretical understanding of why and when it works remains limited. This paper presents analyses for the statistical benefit of multitask representation learning in linear Markov Decision Process (MDP) under a generative model. In this paper, we consider an agent to learn a representation function $\phi$ out of a function class $\Phi$ from $T$ source tasks with $N$ data per task, and then use the learned $\hat{\phi}$ to reduce the required number of sample for a new task. We first discover a \emph{Least-Activated-Feature-Abundance} (LAFA) criterion, denoted as $\kappa$, with which we prove that a straightforward least-square algorithm learns a policy which is $\tilde{O}(H^2\sqrt{\frac{\mathcal{C}(\Phi)^2 \kappa d}{NT}+\frac{\kappa d}{n}})$ sub-optimal. Here $H$ is the planning horizon, $\mathcal{C}(\Phi)$ is $\Phi$'s complexity measure, $d$ is the dimension of the representation (usually $d\ll \mathcal{C}(\Phi)$) and $n$ is the number of samples for the new task. Thus the required $n$ is $O(\kappa d H^4)$ for the sub-optimality to be close to zero, which is much smaller than $O(\mathcal{C}(\Phi)^2\kappa d H^4)$ in the setting without multitask representation learning, whose sub-optimality gap is $\tilde{O}(H^2\sqrt{\frac{\kappa \mathcal{C}(\Phi)^2d}{n}})$. This theoretically explains the power of multitask representation learning in reducing sample complexity. Further, we note that to ensure high sample efficiency, the LAFA criterion $\kappa$ should be small. In fact, $\kappa$ varies widely in magnitude depending on the different sampling distribution for new task. This indicates adaptive sampling technique is important to make $\kappa$ solely depend on $d$. Finally, we provide empirical results of a noisy grid-world environment to corroborate our theoretical findings.

Online reinforcement learning (RL) has been widely applied in information processing scenarios, which usually exhibit much uncertainty due to the intrinsic randomness of channels and service demands. In this paper, we consider an un-discounted RL in general Markov decision processes (MDPs) with both endogeneous and exogeneous uncertainty, where both the rewards and state transition probability are unknown to the RL agent and evolve with the time as long as their respective variations do not exceed certain dynamic budget (i.e., upper bound). We first develop a variation-aware Bernstein-based upper confidence reinforcement learning (VB-UCRL), which we allow to restart according to a schedule dependent on the variations. We successfully overcome the challenges due to the exogeneous uncertainty and establish a regret bound of saving at most $\sqrt{S}$ or $S^{\frac{1}{6}}T^{\frac{1}{12}}$ compared with the latest results in the literature, where $S$ denotes the state size of the MDP and $T$ indicates the iteration index of learning steps.

Reinforcement learning (RL) is empirically successful in complex nonlinear Markov decision processes (MDPs) with continuous state spaces. By contrast, the majority of theoretical RL literature requires the MDP to satisfy some form of linear structure, in order to guarantee sample efficient RL. Such efforts typically assume the transition dynamics or value function of the MDP are described by linear functions of the state features. To resolve this discrepancy between theory and practice, we introduce the Effective Planning Window (EPW) condition, a structural condition on MDPs that makes no linearity assumptions. We demonstrate that the EPW condition permits sample efficient RL, by providing an algorithm which provably solves MDPs satisfying this condition. Our algorithm requires minimal assumptions on the policy class, which can include multi-layer neural networks with nonlinear activation functions. Notably, the EPW condition is directly motivated by popular gaming benchmarks, and we show that many classic Atari games satisfy this condition. We additionally show the necessity of conditions like EPW, by demonstrating that simple MDPs with slight nonlinearities cannot be solved sample efficiently.