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 Markov Models


Attention Is Not All You Need Anymore

arXiv.org Artificial Intelligence

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.


Conformal Off-Policy Evaluation in Markov Decision Processes

arXiv.org Artificial Intelligence

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.


A State-Space Perspective on Modelling and Inference for Online Skill Rating

arXiv.org Machine Learning

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.


Toward Unlimited Self-Learning MCMC with Parallel Adaptive Annealing

arXiv.org Machine Learning

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.


Exploring and Learning in Sparse Linear MDPs without Computationally Intractable Oracles

arXiv.org Machine Learning

The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are linear functions in this representation. But where do these features come from? In the absence of expert domain knowledge, a tempting strategy is to use the ``kitchen sink" approach and hope that the true features are included in a much larger set of potential features. In this paper we revisit linear MDPs from the perspective of feature selection. In a $k$-sparse linear MDP, there is an unknown subset $S \subset [d]$ of size $k$ containing all the relevant features, and the goal is to learn a near-optimal policy in only poly$(k,\log d)$ interactions with the environment. Our main result is the first polynomial-time algorithm for this problem. In contrast, earlier works either made prohibitively strong assumptions that obviated the need for exploration, or required solving computationally intractable optimization problems. Along the way we introduce the notion of an emulator: a succinct approximate representation of the transitions that suffices for computing certain Bellman backups. Since linear MDPs are a non-parametric model, it is not even obvious whether polynomial-sized emulators exist. We show that they do exist and can be computed efficiently via convex programming. As a corollary of our main result, we give an algorithm for learning a near-optimal policy in block MDPs whose decoding function is a low-depth decision tree; the algorithm runs in quasi-polynomial time and takes a polynomial number of samples. This can be seen as a reinforcement learning analogue of classic results in computational learning theory. Furthermore, it gives a natural model where improving the sample complexity via representation learning is computationally feasible.


Generalization through Diversity: Improving Unsupervised Environment Design

arXiv.org Artificial Intelligence

Agent decision making using Reinforcement Learning (RL) heavily relies on either a model or simulator of the environment (e.g., moving in an 8x8 maze with three rooms, playing Chess on an 8x8 board). Due to this dependence, small changes in the environment (e.g., positions of obstacles in the maze, size of the board) can severely affect the effectiveness of the policy learned by the agent. To that end, existing work has proposed training RL agents on an adaptive curriculum of environments (generated automatically) to improve performance on out-of-distribution (OOD) test scenarios. Specifically, existing research has employed the potential for the agent to learn in an environment (captured using Generalized Advantage Estimation, GAE) as the key factor to select the next environment(s) to train the agent. However, such a mechanism can select similar environments (with a high potential to learn) thereby making agent training redundant on all but one of those environments. To that end, we provide a principled approach to adaptively identify diverse environments based on a novel distance measure relevant to environment design. We empirically demonstrate the versatility and effectiveness of our method in comparison to multiple leading approaches for unsupervised environment design on three distinct benchmark problems used in literature.


Exploring the Potential of World Models for Anomaly Detection in Autonomous Driving

arXiv.org Artificial Intelligence

Abstract--In recent years there have been remarkable advancements in autonomous driving. While autonomous vehicles demonstrate high performance in closed-set conditions, they encounter difficulties when confronted with unexpected situations. At the same time, world models emerged in the field of model-based reinforcement learning as a way to enable agents to predict the future depending on potential actions. This led to outstanding results in sparse reward and complex control tasks. This work provides an overview of how world models can be leveraged to perform anomaly detection in the domain of autonomous driving. We provide a characterization of world models and relate individual components to previous works in anomaly detection to facilitate further research in the field.


Crowd-Aware Multi-Agent Pathfinding With Boosted Curriculum Reinforcement Learning

arXiv.org Artificial Intelligence

Multi-Agent Path Finding (MAPF) in crowded environments presents a challenging problem in motion planning, aiming to find collision-free paths for all agents in the system. MAPF finds a wide range of applications in various domains, including aerial swarms, autonomous warehouse robotics, and self-driving vehicles. The current approaches for MAPF can be broadly categorized into two main categories: centralized and decentralized planning. Centralized planning suffers from the curse of dimensionality and thus does not scale well in large and complex environments. On the other hand, decentralized planning enables agents to engage in real-time path planning within a partially observable environment, demonstrating implicit coordination. However, they suffer from slow convergence and performance degradation in dense environments. In this paper, we introduce CRAMP, a crowd-aware decentralized approach to address this problem by leveraging reinforcement learning guided by a boosted curriculum-based training strategy. We test CRAMP on simulated environments and demonstrate that our method outperforms the state-of-the-art decentralized methods for MAPF on various metrics. CRAMP improves the solution quality up to 58% measured in makespan and collision count, and up to 5% in success rate in comparison to previous methods.


Safe POMDP Online Planning via Shielding

arXiv.org Artificial Intelligence

Partially observable Markov decision processes (POMDPs) have been widely used in many robotic applications for sequential decision-making under uncertainty. POMDP online planning algorithms such as Partially Observable Monte-Carlo Planning (POMCP) can solve very large POMDPs with the goal of maximizing the expected return. But the resulting policies cannot provide safety guarantees that are imperative for real-world safety-critical tasks (e.g., autonomous driving). In this work, we consider safety requirements represented as almost-sure reach-avoid specifications (i.e., the probability to reach a set of goal states is one and the probability to reach a set of unsafe states is zero). We compute shields that restrict unsafe actions violating almost-sure reach-avoid specifications. We then integrate these shields into the POMCP algorithm for safe POMDP online planning. We propose four distinct shielding methods, differing in how the shields are computed and integrated, including factored variants designed to improve scalability. Experimental results on a set of benchmark domains demonstrate that the proposed shielding methods successfully guarantee safety (unlike the baseline POMCP without shielding) on large POMDPs, with negligible impact on the runtime for online planning.


Towards Socially Responsive Autonomous Vehicles: A Reinforcement Learning Framework with Driving Priors and Coordination Awareness

arXiv.org Artificial Intelligence

The advent of autonomous vehicles (AVs) alongside human-driven vehicles (HVs) has ushered in an era of mixed traffic flow, presenting a significant challenge: the intricate interaction between these entities within complex driving environments. AVs are expected to have human-like driving behavior to seamlessly integrate into human-dominated traffic systems. To address this issue, we propose a reinforcement learning framework that considers driving priors and Social Coordination Awareness (SCA) to optimize the behavior of AVs. The framework integrates a driving prior learning (DPL) model based on a variational autoencoder to infer the driver's driving priors from human drivers' trajectories. A policy network based on a multi-head attention mechanism is designed to effectively capture the interactive dependencies between AVs and other traffic participants to improve decision-making quality. The introduction of SCA into the autonomous driving decision-making system, and the use of Coordination Tendency (CT) to quantify the willingness of AVs to coordinate the traffic system is explored. Simulation results show that the proposed framework can not only improve the decision-making quality of AVs but also motivate them to produce social behaviors, with potential benefits for the safety and traffic efficiency of the entire transportation system.