Teaching physical skills to humans requires one-on-one interaction between the teacher and the learner. With a shortage of human teachers, such a teaching mode faces the challenge of scaling up. Robots, with their replicable nature and physical capabilities, offer a solution. In this work, we present TeachingBot, a robotic system designed for teaching handwriting to human learners. We tackle two primary challenges in this teaching task: the adaptation to each learner's unique style and the creation of an engaging learning experience. TeachingBot captures the learner's style using a probabilistic learning approach based on the learner's handwriting. Then, based on the learned style, it provides physical guidance to human learners with variable impedance to make the learning experience engaging. Results from human-subject experiments based on 15 human subjects support the effectiveness of TeachingBot, demonstrating improved human learning outcomes compared to baseline methods. Additionally, we illustrate how TeachingBot customizes its teaching approach for individual learners, leading to enhanced overall engagement and effectiveness.

In many branches of engineering, Banach contraction mapping theorem is employed to establish the convergence of certain deterministic algorithms. Randomized versions of these algorithms have been developed that have proved useful in data-driven problems. In a class of randomized algorithms, in each iteration, the contraction map is approximated with an operator that uses independent and identically distributed samples of certain random variables. This leads to iterated random operators acting on an initial point in a complete metric space, and it generates a Markov chain. In this paper, we develop a new stochastic dominance based proof technique, called probabilistic contraction analysis, for establishing the convergence in probability of Markov chains generated by such iterated random operators in certain limiting regime. The methods developed in this paper provides a general framework for understanding convergence of a wide variety of Monte Carlo methods in which contractive property is present. We apply the convergence result to conclude the convergence of fitted value iteration and fitted relative value iteration in continuous state and continuous action Markov decision problems as representative applications of the general framework developed here.

Reinforcement learning is a powerful technique for learning from trial and error, but it often requires a large number of interactions to achieve good performance. In some domains, such as sparse-reward tasks, an oracle that can provide useful feedback or guidance to the agent during the learning process is really of great importance. However, querying the oracle too frequently may be costly or impractical, and the oracle may not always have a clear answer for every situation. Therefore, we propose a novel method for interacting with the oracle in a selective and efficient way, using a retrieval-based approach. We assume that the interaction can be modeled as a sequence of templated questions and answers, and that there is a large corpus of previous interactions available. We use a neural network to encode the current state of the agent and the oracle, and retrieve the most relevant question from the corpus to ask the oracle. We then use the oracle's answer to update the agent's policy and value function. We evaluate our method on an object manipulation task. We show that our method can significantly improve the efficiency of RL by reducing the number of interactions needed to reach a certain level of performance, compared to baselines that do not use the oracle or use it in a naive way.

We investigate the approximation efficiency of score functions by deep neural networks in diffusion-based generative modeling. While existing approximation theories utilize the smoothness of score functions, they suffer from the curse of dimensionality for intrinsically high-dimensional data. This limitation is pronounced in graphical models such as Markov random fields, common for image distributions, where the approximation efficiency of score functions remains unestablished. To address this, we observe score functions can often be well-approximated in graphical models through variational inference denoising algorithms. Furthermore, these algorithms are amenable to efficient neural network representation. We demonstrate this in examples of graphical models, including Ising models, conditional Ising models, restricted Boltzmann machines, and sparse encoding models. Combined with off-the-shelf discretization error bounds for diffusion-based sampling, we provide an efficient sample complexity bound for diffusion-based generative modeling when the score function is learned by deep neural networks.

This paper introduces a novel backup strategy for Monte-Carlo Tree Search (MCTS) designed for highly stochastic and partially observable Markov decision processes. We adopt a probabilistic approach, modeling both value and action-value nodes as Gaussian distributions. We introduce a novel backup operator that computes value nodes as the Wasserstein barycenter of their action-value children nodes; thus, propagating the uncertainty of the estimate across the tree to the root node. We study our novel backup operator when using a novel combination of $L^1$-Wasserstein barycenter with $\alpha$-divergence, by drawing a notable connection to the generalized mean backup operator. We complement our probabilistic backup operator with two sampling strategies, based on optimistic selection and Thompson sampling, obtaining our Wasserstein MCTS algorithm. We provide theoretical guarantees of asymptotic convergence to the optimal policy, and an empirical evaluation on several stochastic and partially observable environments, where our approach outperforms well-known related baselines.

Decision making under uncertainty is at the heart of any autonomous system acting with imperfect information. The cost of solving the decision making problem is exponential in the action and observation spaces, thus rendering it unfeasible for many online systems. This paper introduces a novel approach to efficient decision-making, by partitioning the high-dimensional observation space. Using the partitioned observation space, we formulate analytical bounds on the expected information-theoretic reward, for general belief distributions. These bounds are then used to plan efficiently while keeping performance guarantees. We show that the bounds are adaptive, computationally efficient, and that they converge to the original solution. We extend the partitioning paradigm and present a hierarchy of partitioned spaces that allows greater efficiency in planning. We then propose a specific variant of these bounds for Gaussian beliefs and show a theoretical performance improvement of at least a factor of 4. Finally, we compare our novel method to other state of the art algorithms in active SLAM scenarios, in simulation and in real experiments. In both cases we show a significant speed-up in planning with performance guarantees.

In recent years, the popular Transformer architecture has achieved great success in many application areas, including natural language processing and computer vision. Many existing works aim to reduce the computational and memory complexity of the self-attention mechanism in the Transformer by trading off performance. However, performance is key for the continuing success of the Transformer. In this paper, a family of drop-in replacements for the self-attention mechanism in the Transformer, called the Extractors, is proposed. Four types of the Extractors, namely the super high-performance Extractor (SHE), the higher-performance Extractor (HE), the worthwhile Extractor (WE), and the minimalist Extractor (ME), are proposed as examples. Experimental results show that replacing the self-attention mechanism with the SHE evidently improves the performance of the Transformer, whereas the simplified versions of the SHE, i.e., the HE, the WE, and the ME, perform close to or better than the self-attention mechanism with less computational and memory complexity. Furthermore, the proposed Extractors have the potential or are able to run faster than the self-attention mechanism since their critical paths of computation are much shorter. Additionally, the sequence prediction problem in the context of text generation is formulated using variable-length discrete-time Markov chains, and the Transformer is reviewed based on our understanding.

Reinforcement Learning aims at identifying and evaluating efficient control policies from data. In many real-world applications, the learner is not allowed to experiment and cannot gather data in an online manner (this is the case when experimenting is expensive, risky or unethical). For such applications, the reward of a given policy (the target policy) must be estimated using historical data gathered under a different policy (the behavior policy). Most methods for this learning task, referred to as Off-Policy Evaluation (OPE), do not come with accuracy and certainty guarantees. We present a novel OPE method based on Conformal Prediction that outputs an interval containing the true reward of the target policy with a prescribed level of certainty. The main challenge in OPE stems from the distribution shift due to the discrepancies between the target and the behavior policies. We propose and empirically evaluate different ways to deal with this shift. Some of these methods yield conformalized intervals with reduced length compared to existing approaches, while maintaining the same certainty level.

In the quantitative analysis of competitive sports, a fundamental task is to estimate the skills of the different agents ('players') involved in a given competition based on the outcome of pairwise comparisons ('matches') between said players, often in an online setting. Skill estimation facilitates the prediction of various relevant outcomes of subsequent matches, which can then be applied towards high-level decision-making for the competition, including player seeding, fair team matching, and more. There are several established approaches to the task of skill estimation, including among others the Bradley-Terry model (Bradley and Terry, 1952), the Elo rating system (Elo, 1978), the Glicko rating system (Glickman, 1999), and TrueSkill (Herbrich et al., 2006) each with various levels of complexity and varying degrees of statistical motivation. Skill rating is of paramount importance in the world of competitive sports as it serves as a foundational tool for assessing and comparing the abilities of players and how they vary over time. By accurately quantifying skill levels, skill rating systems enable fair and balanced competition, inform strategic decision-making, and enhance the overall sporting level.

Its efficiency strongly depends on the choice of the proposal. Self-learning Monte Carlo (SLMC) methods are recently proposed to accelerate Markov chain Among recent advances in machine learning, a general Monte Carlo (MCMC) methods using a machine method called the self-learning Monte Carlo (SLMC) learning model. With latent generative models, method (Liu et al., 2017) was introduced to accelerate SLMC methods realize efficient Monte Carlo updates MCMC simulations by an automated proposal with a machine with less autocorrelation. However, SLMC learning model and has been applied to various problems methods are difficult to directly apply to multimodal (Xu et al., 2017; Shen et al., 2018). In particular, distributions for which training data are a latent generative model realizes efficient global update difficult to obtain. To solve the limitation, we propose through the obtained information-rich latent representation "parallel adaptive annealing," which makes (Huang & Wang, 2017; Albergo et al., 2019; Monroe & SLMC methods directly apply to multimodal distributions Shen, 2022; Tanaka & Tomiya, 2017). Although powerful, with a gradually trained proposal while the performance of SLMC simulation strongly depends annealing target distribution. Parallel adaptive annealing on an automated proposal with machine learning models is based on (i) sequential learning with and the quality of training data to train the proposal. For annealing to inherit and update the model parameters, example, it is challenging to directly use SLMC for multimodal (ii) adaptive annealing to automatically detect distributions because obtaining accurate training data under-learning, and (iii) parallel annealing to covering all modes is difficult.