The Baum-Welch (B-W) algorithm is the most widely accepted method for inferring hidden Markov models (HMM). However, it is prone to getting stuck in local optima, and can be too slow for many real-time applications. Spectral learning of HMMs (SHMM), based on the method of moments (MOM) has been proposed in the literature to overcome these obstacles. Despite its promises, asymptotic theory for SHMM has been elusive, and the long-run performance of SHMM can degrade due to unchecked propagation of error. In this paper, we (1) provide an asymptotic distribution for the approximate error of the likelihood estimated by SHMM, (2) propose a novel algorithm called projected SHMM (PSHMM) that mitigates the problem of error propagation, and (3) develop online learning variants of both SHMM and PSHMM that accommodate potential nonstationarity. We compare the performance of SHMM with PSHMM and estimation through the B-W algorithm on both simulated data and data from real world applications, and find that PSHMM not only retains the computational advantages of SHMM, but also provides more robust estimation and forecasting.

In high performance systems it is sometimes hard to build very large graphs that are efficient both with respect to memory and compute. This paper proposes a data structure called Markov-chain-priority-queue (MCPrioQ), which is a lock-free sparse markov-chain that enables online and continuous learning with time-complexity of $O(1)$ for updates and $O(CDF^{-1}(t))$ inference. MCPrioQ is especially suitable for recommender-systems for lookups of $n$-items in descending probability order. The concurrent updates are achieved using hash-tables and atomic instructions and the lookups are achieved through a novel priority-queue which allows for approximately correct results even during concurrent updates. The approximatly correct and lock-free property is maintained by a read-copy-update scheme, but where the semantics have been slightly updated to allow for swap of elements rather than the traditional pop-insert scheme.

Centralized training with decentralized execution (CTDE) is a widely-used learning paradigm that has achieved significant success in complex tasks. However, partial observability issues and the absence of effectively shared signals between agents often limit its effectiveness in fostering cooperation. While communication can address this challenge, it simultaneously reduces the algorithm's practicality. Drawing inspiration from human team cooperative learning, we propose a novel paradigm that facilitates a gradual shift from explicit communication to tacit cooperation. In the initial training stage, we promote cooperation by sharing relevant information among agents and concurrently reconstructing this information using each agent's local trajectory. We then combine the explicitly communicated information with the reconstructed information to obtain mixed information. Throughout the training process, we progressively reduce the proportion of explicitly communicated information, facilitating a seamless transition to fully decentralized execution without communication. Experimental results in various scenarios demonstrate that the performance of our method without communication can approaches or even surpasses that of QMIX and communication-based methods.

In this paper, we investigate the scheduling issue of diesel generators (DGs) in an Internet of Things (IoT)-Driven isolated microgrid (MG) by deep reinforcement learning (DRL). The renewable energy is fully exploited under the uncertainty of renewable generation and load demand. The DRL agent learns an optimal policy from history renewable and load data of previous days, where the policy can generate real-time decisions based on observations of past renewable and load data of previous hours collected by connected sensors. The goal is to reduce operating cost on the premise of ensuring supply-demand balance. In specific, a novel finite-horizon partial observable Markov decision process (POMDP) model is conceived considering the spinning reserve. In order to overcome the challenge of discrete-continuous hybrid action space due to the binary DG switching decision and continuous energy dispatch (ED) decision, a DRL algorithm, namely the hybrid action finite-horizon RDPG (HAFH-RDPG), is proposed. HAFH-RDPG seamlessly integrates two classical DRL algorithms, i.e., deep Q-network (DQN) and recurrent deterministic policy gradient (RDPG), based on a finite-horizon dynamic programming (DP) framework. Extensive experiments are performed with real-world data in an IoT-driven MG to evaluate the capability of the proposed algorithm in handling the uncertainty due to inter-hour and inter-day power fluctuation and to compare its performance with those of the benchmark algorithms. J. Qi, L. Lei, and S. X. Yang are with the School of Engineering, University of Guelph, Guelph, ON N1G 2W1, Canada (e-mail: jiaju@uoguelph.ca; K. Zheng is with the College of Electrical Engineering and Computer Sciences, Ningbo University, Ningbo, 315211, China.

Model Predictive Control (MPC) is attracting tremendous attention in the autonomous driving task as a powerful control technique. The success of an MPC controller strongly depends on an accurate internal dynamics model. However, the static parameters, usually learned by system identification, often fail to adapt to both internal and external perturbations in real-world scenarios. In this paper, we firstly (1) reformulate the problem as a Partially Observed Markov Decision Process (POMDP) that absorbs the uncertainties into observations and maintains Markov property into hidden states; and (2) learn a recurrent policy continually adapting the parameters of the dynamics model via Recurrent Reinforcement Learning (RRL) for optimal and adaptive control; and (3) finally evaluate the proposed algorithm (referred as $\textit{MPC-RRL}$) in CARLA simulator and leading to robust behaviours under a wide range of perturbations.

Model distillation has been a popular method for producing interpretable machine learning. It uses an interpretable "student" model to mimic the predictions made by the black box "teacher" model. However, when the student model is sensitive to the variability of the data sets used for training even when keeping the teacher fixed, the corresponded interpretation is not reliable. Existing strategies stabilize model distillation by checking whether a large enough corpus of pseudo-data is generated to reliably reproduce student models, but methods to do so have so far been developed for a specific student model. In this paper, we develop a generic approach for stable model distillation based on central limit theorem for the average loss. We start with a collection of candidate student models and search for candidates that reasonably agree with the teacher. Then we construct a multiple testing framework to select a corpus size such that the consistent student model would be selected under different pseudo samples. We demonstrate the application of our proposed approach on three commonly used intelligible models: decision trees, falling rule lists and symbolic regression. Finally, we conduct simulation experiments on Mammographic Mass and Breast Cancer datasets and illustrate the testing procedure throughout a theoretical analysis with Markov process. The code is publicly available at https://github.com/yunzhe-zhou/GenericDistillation.

We study online learning in episodic constrained Markov decision processes (CMDPs), where the goal of the learner is to collect as much reward as possible over the episodes, while guaranteeing that some long-term constraints are satisfied during the learning process. Rewards and constraints can be selected either stochastically or adversarially, and the transition function is not known to the learner. While online learning in classical unconstrained MDPs has received considerable attention over the last years, the setting of CMDPs is still largely unexplored. This is surprising, since in real-world applications, such as, e.g., autonomous driving, automated bidding, and recommender systems, there are usually additional constraints and specifications that an agent has to obey during the learning process. In this paper, we provide the first best-of-both-worlds algorithm for CMDPs with long-term constraints. Our algorithm is capable of handling settings in which rewards and constraints are selected either stochastically or adversarially, without requiring any knowledge of the underling process. Moreover, our algorithm matches state-of-the-art regret and constraint violation bounds for settings in which constraints are selected stochastically, while it is the first to provide guarantees in the case in which they are chosen adversarially.

Large language models (LLMs) are known for their exceptional performance in natural language processing, making them highly effective in many human life-related or even job-related tasks. The attention mechanism in the Transformer architecture is a critical component of LLMs, as it allows the model to selectively focus on specific input parts. The softmax unit, which is a key part of the attention mechanism, normalizes the attention scores. Hence, the performance of LLMs in various NLP tasks depends significantly on the crucial role played by the attention mechanism with the softmax unit. In-context learning, as one of the celebrated abilities of recent LLMs, is an important concept in querying LLMs such as ChatGPT. Without further parameter updates, Transformers can learn to predict based on few in-context examples. However, the reason why Transformers becomes in-context learners is not well understood. Recently, several works [ASA+22,GTLV22,ONR+22] have studied the in-context learning from a mathematical perspective based on a linear regression formulation $\min_x\| Ax - b \|_2$, which show Transformers' capability of learning linear functions in context. In this work, we study the in-context learning based on a softmax regression formulation $\min_{x} \| \langle \exp(Ax), {\bf 1}_n \rangle^{-1} \exp(Ax) - b \|_2$ of Transformer's attention mechanism. We show the upper bounds of the data transformations induced by a single self-attention layer and by gradient-descent on a $\ell_2$ regression loss for softmax prediction function, which imply that when training self-attention-only Transformers for fundamental regression tasks, the models learned by gradient-descent and Transformers show great similarity.

Many games feature a progression of levels that doesn't adapt to the player. This can be problematic because some players may get stuck if the progression is too difficult, while others may find it boring if the progression is too slow to get to more challenging levels. This can be addressed by building levels based on the player's performance and preferences. In this work, we formulate the problem of generating levels for a player as a Markov Decision Process (MDP) and use adaptive dynamic programming (ADP) to solve the MDP before assembling a level. We tested with two case studies and found that using an ADP outperforms two baselines. Furthermore, we experimented with player proxies and switched them in the middle of play, and we show that a simple modification prior to running ADP results in quick adaptation. By using ADP, which searches the entire MDP, we produce a dynamic progression of levels that adapts to the player.

We investigate whether Deep Reinforcement Learning (Deep RL) is able to synthesize sophisticated and safe movement skills for a low-cost, miniature humanoid robot that can be composed into complex behavioral strategies in dynamic environments. We used Deep RL to train a humanoid robot with 20 actuated joints to play a simplified one-versus-one (1v1) soccer game. We first trained individual skills in isolation and then composed those skills end-to-end in a self-play setting. The resulting policy exhibits robust and dynamic movement skills such as rapid fall recovery, walking, turning, kicking and more; and transitions between them in a smooth, stable, and efficient manner - well beyond what is intuitively expected from the robot. The agents also developed a basic strategic understanding of the game, and learned, for instance, to anticipate ball movements and to block opponent shots. The full range of behaviors emerged from a small set of simple rewards. Our agents were trained in simulation and transferred to real robots zero-shot. We found that a combination of sufficiently high-frequency control, targeted dynamics randomization, and perturbations during training in simulation enabled good-quality transfer, despite significant unmodeled effects and variations across robot instances. Although the robots are inherently fragile, minor hardware modifications together with basic regularization of the behavior during training led the robots to learn safe and effective movements while still performing in a dynamic and agile way. Indeed, even though the agents were optimized for scoring, in experiments they walked 156% faster, took 63% less time to get up, and kicked 24% faster than a scripted baseline, while efficiently combining the skills to achieve the longer term objectives. Examples of the emergent behaviors and full 1v1 matches are available on the supplementary website.