We consider approximate dynamic programming in $\gamma$-discounted Markov decision processes and apply it to approximate planning with linear value-function approximation. Our first contribution is a new variant of Approximate Policy Iteration (API), called Confident Approximate Policy Iteration (CAPI), which computes a deterministic stationary policy with an optimal error bound scaling linearly with the product of the effective horizon $H$ and the worst-case approximation error $\epsilon$ of the action-value functions of stationary policies. This improvement over API (whose error scales with $H^2$) comes at the price of an $H$-fold increase in memory cost. Unlike Scherrer and Lesner [2012], who recommended computing a non-stationary policy to achieve a similar improvement (with the same memory overhead), we are able to stick to stationary policies. This allows for our second contribution, the application of CAPI to planning with local access to a simulator and $d$-dimensional linear function approximation. As such, we design a planning algorithm that applies CAPI to obtain a sequence of policies with successively refined accuracies on a dynamically evolving set of states. The algorithm outputs an $\tilde O(\sqrt{d}H\epsilon)$-optimal policy after issuing $\tilde O(dH^4/\epsilon^2)$ queries to the simulator, simultaneously achieving the optimal accuracy bound and the best known query complexity bound, while earlier algorithms in the literature achieve only one of them. This query complexity is shown to be tight in all parameters except $H$. These improvements come at the expense of a mild (polynomial) increase in memory and computational costs of both the algorithm and its output policy.

We propose a general framework for policy representation for reinforcement learning tasks. This framework involves finding a low-dimensional embedding of the policy on a reproducing kernel Hilbert space (RKHS). The usage of RKHS based methods allows us to derive strong theoretical guarantees on the expected return of the reconstructed policy. Such guarantees are typically lacking in black-box models, but are very desirable in tasks requiring stability and convergence guarantees. We conduct several experiments on classic RL domains. The results confirm that the policies can be robustly represented in a low-dimensional space while the embedded policy incurs almost no decrease in returns.

This paper consists of a collection of (mostly) pen-and-paper exercises in machine learning. The exercises are on the following topics: linear algebra, optimization, directed graphical models, undirected graphical models, expressive power of graphical models, factor graphs and message passing, inference for hidden Markov models, model-based learning (including ICA and unnormalized models), sampling and Monte-Carlo integration, and variational inference. Highly recommended for data scientists wishing to evolve their understanding of the mathematical foundations of the field.

Streaming keyword spotting is a widely used solution for activating voice assistants. Deep Neural Networks with Hidden Markov Model (DNN-HMM) based methods have proven to be efficient and widely adopted in this space, primarily because of the ability to detect and identify the start and end of the wake-up word at low compute cost. However, such hybrid systems suffer from loss metric mismatch when the DNN and HMM are trained independently. Sequence discriminative training cannot fully mitigate the loss-metric mismatch due to the inherent Markovian style of the operation. We propose an low footprint CNN model, called HEiMDaL, to detect and localize keywords in streaming conditions. We introduce an alignment-based classification loss to detect the occurrence of the keyword along with an offset loss to predict the start of the keyword. HEiMDaL shows 73% reduction in detection metrics along with equivalent localization accuracy and with the same memory footprint as existing DNN-HMM style models for a given wake-word.

State-of-the-art methods for solving 2-player zero-sum imperfect information games rely on linear programming or regret minimization, though not on dynamic programming (DP) or heuristic search (HS), while the latter are often at the core of state-of-the-art solvers for other sequential decision-making problems. In partially observable or collaborative settings (e.g., POMDPs and Dec- POMDPs), DP and HS require introducing an appropriate statistic that induces a fully observable problem as well as bounding (convex) approximators of the optimal value function. This approach has succeeded in some subclasses of 2-player zero-sum partially observable stochastic games (zs- POSGs) as well, but how to apply it in the general case still remains an open question. We answer it by (i) rigorously defining an equivalent game to work with, (ii) proving mathematical properties of the optimal value function that allow deriving bounds that come with solution strategies, (iii) proposing for the first time an HSVI-like solver that provably converges to an $\epsilon$-optimal solution in finite time, and (iv) empirically analyzing it. This opens the door to a novel family of promising approaches complementing those relying on linear programming or iterative methods.

In this paper, for POMDPs, we provide the convergence of a Q learning algorithm for control policies using a finite history of past observations and control actions, and, consequentially, we establish near optimality of such limit Q functions under explicit filter stability conditions. We present explicit error bounds relating the approximation error to the length of the finite history window. We establish the convergence of such Q-learning iterations under mild ergodicity assumptions on the state process during the exploration phase. We further show that the limit fixed point equation gives an optimal solution for an approximate belief-MDP. We then provide bounds on the performance of the policy obtained using the limit Q values compared to the performance of the optimal policy for the POMDP, where we also present explicit conditions using recent results on filter stability in controlled POMDPs. While there exist many experimental results, (i) the rigorous asymptotic convergence (to an approximate MDP value function) for such finite-memory Q-learning algorithms, and (ii) the near optimality with an explicit rate of convergence (in the memory size) are results that are new to the literature, to our knowledge.

We propose Algorithm Distillation (AD), a method for distilling reinforcement learning (RL) algorithms into neural networks by modeling their training histories with a causal sequence model. Algorithm Distillation treats learning to reinforcement learn as an across-episode sequential prediction problem. A dataset of learning histories is generated by a source RL algorithm, and then a causal transformer is trained by autoregressively predicting actions given their preceding learning histories as context. Unlike sequential policy prediction architectures that distill post-learning or expert sequences, AD is able to improve its policy entirely in-context without updating its network parameters. We demonstrate that AD can reinforcement learn in-context in a variety of environments with sparse rewards, combinatorial task structure, and pixel-based observations, and find that AD learns a more data-efficient RL algorithm than the one that generated the source data. Algorithm Distillation (AD) has two steps - (i) a dataset of learning histories is collected from individual single-task RL algorithms solving different tasks; (ii) a causal transformer predicts actions from these histories using across-episodic contexts. Since the RL policy improves throughout the learning histories, by predicting actions accurately AD learns to output an improved policy relative to the one seen in its context. AD models state-action-reward tokens, and does not condition on returns. Transformers have emerged as powerful neural network architectures for sequence modeling (Vaswani et al., 2017). A striking property of pre-trained transformers is their ability to adapt to downstream tasks through prompt conditioning or in-context learning. After pre-training on large offline datasets, large transformers have been shown to generalize to downstream tasks in text completion (Brown et al., 2020), language understanding (Devlin et al., 2018), and image generation (Yu et al., 2022). Recent work demonstrated that transformers can also learn policies from offline data by treating offline Reinforcement Learning (RL) as a sequential prediction problem. While Chen et al. (2021) showed that transformers can learn single-task policies from offline RL data via imitation learning, subsequent work showed that transformers can also extract multi-task policies in both same-domain (Lee et al., 2022) and cross-domain settings (Reed et al., 2022).

Most previous neural text-to-speech (TTS) methods are mainly based on supervised learning methods, which means they depend on a large training dataset and hard to achieve comparable performance under low-resource conditions. To address this issue, we propose a semi-supervised learning method for neural TTS in which labeled target data is limited, which can also resolve the problem of exposure bias in the previous auto-regressive models. Specifically, we pre-train the reference model based on Fastspeech2 with much source data, fine-tuned on a limited target dataset. Meanwhile, pseudo labels generated by the original reference model are used to guide the fine-tuned model's training further, achieve a regularization effect, and reduce the overfitting of the fine-tuned model during training on the limited target data. Experimental results show that our proposed semi-supervised learning scheme with limited target data significantly improves the voice quality for test data to achieve naturalness and robustness in speech synthesis.

The ability to direct a Probabilistic Boolean Network (PBN) to a desired state is important to applications such as targeted therapeutics in cancer biology. Reinforcement Learning (RL) has been proposed as a framework that solves a discrete-time optimal control problem cast as a Markov Decision Process. We focus on an integrative framework powered by a model-free deep RL method that can address different flavours of the control problem (e.g., with or without control inputs; attractor state or a subset of the state space as the target domain). The method is agnostic to the distribution of probabilities for the next state, hence it does not use the probability transition matrix. The time complexity is linear on the time steps, or interactions between the agent (deep RL) and the environment (PBN), during training. Indeed, we explore the scalability of the deep RL approach to (set) stabilization of large-scale PBNs and demonstrate successful control on large networks, including a metastatic melanoma PBN with 200 nodes.

We consider the problem of simultaneous learning in stochastic games with many players in the finite-horizon setting. While the typical target solution for a stochastic game is a Nash equilibrium, this is intractable with many players. We instead focus on variants of {\it correlated equilibria}, such as those studied for extensive-form games. We begin with a hardness result for the adversarial MDP problem: even for a horizon of 3, obtaining sublinear regret against the best non-stationary policy is \textsf{NP}-hard when both rewards and transitions are adversarial. This implies that convergence to even the weakest natural solution concept -- normal-form coarse correlated equilbrium -- is not possible via black-box reduction to a no-regret algorithm even in stochastic games with constant horizon (unless $\textsf{NP}\subseteq\textsf{BPP}$). Instead, we turn to a different target: algorithms which {\it generate} an equilibrium when they are used by all players. Our main result is algorithm which generates an {\it extensive-form} correlated equilibrium, whose runtime is exponential in the horizon but polynomial in all other parameters. We give a similar algorithm which is polynomial in all parameters for "fast-mixing" stochastic games. We also show a method for efficiently reaching normal-form coarse correlated equilibria in "single-controller" stochastic games which follows the traditional no-regret approach. When shared randomness is available, the two generative algorithms can be extended to give simultaneous regret bounds and converge in the traditional sense.