Digital twins (DTs) have emerged as a promising enabler for representing the real-time states of physical worlds and realizing self-sustaining systems. In practice, DTs of physical devices, such as mobile users (MUs), are commonly deployed in multi-access edge computing (MEC) networks for the sake of reducing latency. To ensure the accuracy and fidelity of DTs, it is essential for MUs to regularly synchronize their status with their DTs. However, MU mobility introduces significant challenges to DT synchronization. Firstly, MU mobility triggers DT migration which could cause synchronization failures. Secondly, MUs require frequent synchronization with their DTs to ensure DT fidelity. Nonetheless, DT migration among MEC servers, caused by MU mobility, may occur infrequently. Accordingly, we propose a two-timescale DT synchronization and migration framework with reliability consideration by establishing a non-convex stochastic problem to minimize the long-term average energy consumption of MUs. We use Lyapunov theory to convert the reliability constraints and reformulate the new problem as a partially observable Markov decision-making process (POMDP). Furthermore, we develop a heterogeneous agent proximal policy optimization with Beta distribution (Beta-HAPPO) method to solve it. Numerical results show that our proposed Beta-HAPPO method achieves significant improvements in energy savings when compared with other benchmarks.

Designing a safe policy for uncertain environments is crucial in real-world control applications. However, this challenge remains inadequately addressed within the Markov decision process (MDP) framework. This paper presents the first algorithm capable of identifying a near-optimal policy in a robust constrained MDP (RCMDP), where an optimal policy minimizes cumulative cost while satisfying constraints in the worst-case scenario across a set of environments. We first prove that the conventional Lagrangian max-min formulation with policy gradient methods can become trapped in suboptimal solutions by encountering a sum of conflicting gradients from the objective and constraint functions during its inner minimization problem. To address this, we leverage the epigraph form of the RCMDP problem, which resolves the conflict by selecting a single gradient from either the objective or the constraints. Building on the epigraph form, we propose a binary search algorithm with a policy gradient subroutine and prove that it identifies an $\varepsilon$-optimal policy in an RCMDP with $\tilde{\mathcal{O}}(\varepsilon^{-4})$ policy evaluations.

Recurrent Neural Networks (RNNs) are used to learn representations in partially observable environments. For agents that learn online and continually interact with the environment, it is desirable to train RNNs with real-time recurrent learning (RTRL); unfortunately, RTRL is prohibitively expensive for standard RNNs. A promising direction is to use linear recurrent architectures (LRUs), where dense recurrent weights are replaced with a complex-valued diagonal, making RTRL efficient. In this work, we build on these insights to provide a lightweight but effective approach for training RNNs in online RL. We introduce Recurrent Trace Units (RTUs), a small modification on LRUs that we nonetheless find to have significant performance benefits over LRUs when trained with RTRL. We find RTUs significantly outperform other recurrent architectures across several partially observable environments while using significantly less computation.

In visual Reinforcement Learning (RL), learning from pixel-based observations poses significant challenges on sample efficiency, primarily due to the complexity of extracting informative state representations from high-dimensional data. Previous methods such as contrastive-based approaches have made strides in improving sample efficiency but fall short in modeling the nuanced evolution of states. To address this, we introduce MOOSS, a novel framework that leverages a temporal contrastive objective with the help of graph-based spatial-temporal masking to explicitly model state evolution in visual RL. Specifically, we propose a self-supervised dual-component strategy that integrates (1) a graph construction of pixel-based observations for spatial-temporal masking, coupled with (2) a multi-level contrastive learning mechanism that enriches state representations by emphasizing temporal continuity and change of states. MOOSS advances the understanding of state dynamics by disrupting and learning from spatial-temporal correlations, which facilitates policy learning. Our comprehensive evaluation on multiple continuous and discrete control benchmarks shows that MOOSS outperforms previous state-of-the-art visual RL methods in terms of sample efficiency, demonstrating the effectiveness of our method. Our code is released at https://github.com/jsun57/MOOSS.

In this paper, we study the shortest path problem (SPP) with multiple source-destination pairs (MSD), namely MSD-SPP, to minimize average travel time of all shortest paths. The inherent traffic capacity limits within a road network contributes to the competition among vehicles. Multi-agent reinforcement learning (MARL) model cannot offer effective and efficient path planning cooperation due to the asynchronous decision making setting in MSD-SPP, where vehicles (a.k.a agents) cannot simultaneously complete routing actions in the previous time step. To tackle the efficiency issue, we propose to divide an entire road network into multiple sub-graphs and subsequently execute a two-stage process of inter-region and intra-region route planning. To address the asynchronous issue, in the proposed asyn-MARL framework, we first design a global state, which exploits a low-dimensional vector to implicitly represent the joint observations and actions of multi-agents. Then we develop a novel trajectory collection mechanism to decrease the redundancy in training trajectories. Additionally, we design a novel actor network to facilitate the cooperation among vehicles towards the same or close destinations and a reachability graph aimed at preventing infinite loops in routing paths. On both synthetic and real road networks, our evaluation result demonstrates that our approach outperforms state-of-the-art planning approaches.

In this survey, we design formal verification and control algorithms for autonomous systems with practical safety guarantees using conformal prediction (CP), a statistical tool for uncertainty quantification. We focus on learning-enabled autonomous systems (LEASs) in which the complexity of learning-enabled components (LECs) is a major bottleneck that hampers the use of existing model-based verification and design techniques. Instead, we advocate for the use of CP, and we will demonstrate its use in formal verification, systems and control theory, and robotics. We argue that CP is specifically useful due to its simplicity (easy to understand, use, and modify), generality (requires no assumptions on learned models and data distributions, i.e., is distribution-free), and efficiency (real-time capable and accurate). We pursue the following goals with this survey. First, we provide an accessible introduction to CP for non-experts who are interested in using CP to solve problems in autonomy. Second, we show how to use CP for the verification of LECs, e.g., for verifying input-output properties of neural networks. Third and fourth, we review recent articles that use CP for safe control design as well as offline and online verification of LEASs. We summarize their ideas in a unifying framework that can deal with the complexity of LEASs in a computationally efficient manner. In our exposition, we consider simple system specifications, e.g., robot navigation tasks, as well as complex specifications formulated in temporal logic formalisms. Throughout our survey, we compare to other statistical techniques (e.g., scenario optimization, PAC-Bayes theory, etc.) and how these techniques have been used in verification and control. Lastly, we point the reader to open problems and future research directions.

Diffusion models have emerged from various theoretical and methodological perspectives, each offering unique insights into their underlying principles. In this work, we provide an overview of the most prominent approaches, drawing attention to their striking analogies - namely, how seemingly diverse methodologies converge to a similar mathematical formulation of the core problem. While our ultimate goal is to understand these models in the context of graphs, we begin by conducting experiments in a simpler setting to build foundational insights. Through an empirical investigation of different diffusion and sampling techniques, we explore three critical questions: (1) What role does noise play in these models? Our findings aim to enhance the understanding of diffusion models and in the long run their application in graph machine learning. The forward process is modelled by a Markov process. The reverse process is unknown and needs to be approximated; this is usually done with a neural network. Consider the analogy of dropping a small amount of paint into a glass of water. Initially, the paint is concentrated in one location, but over time, it diffuses throughout the water until it reaches a state of equilibrium.

Deep Learning algorithms, such as those used in Reinforcement Learning, often require large quantities of data to train effectively. In most cases, the availability of data is not a significant issue. However, for some contexts, such as in autonomous cyber defence, we require data efficient methods. Recently, Quantum Machine Learning and Boltzmann Machines have been proposed as solutions to this challenge. In this work we build upon the pre-existing work to extend the use of Deep Boltzmann Machines to the cutting edge algorithm Proximal Policy Optimisation in a Reinforcement Learning cyber defence environment. We show that this approach, when solved using a D-WAVE quantum annealer, can lead to a two-fold increase in data efficiency. We therefore expect it to be used by the machine learning and quantum communities who are hoping to capitalise on data-efficient Reinforcement Learning methods.

This paper analyzes reinforcement learning (RL) algorithms for Markov decision processes (MDPs) under the average-reward criterion. We focus on Q-learning algorithms based on relative value iteration (RVI), which are model-free stochastic analogues of the classical RVI method for average-reward MDPs. These algorithms have low per-iteration complexity, making them well-suited for large state space problems. We extend the almost-sure convergence analysis of RVI Q-learning algorithms developed by Abounadi, Bertsekas, and Borkar (2001) from unichain to weakly communicating MDPs. This extension is important both practically and theoretically: weakly communicating MDPs cover a much broader range of applications compared to unichain MDPs, and their optimality equations have a richer solution structure (with multiple degrees of freedom), introducing additional complexity in proving algorithmic convergence. We also characterize the sets to which RVI Q-learning algorithms converge, showing that they are compact, connected, potentially nonconvex, and comprised of solutions to the average-reward optimality equation, with exactly one less degree of freedom than the general solution set of this equation. Furthermore, we extend our analysis to two RVI-based hierarchical average-reward RL algorithms using the options framework, proving their almost-sure convergence and characterizing their sets of convergence under the assumption that the underlying semi-Markov decision process is weakly communicating.

What data or environments to use for training to improve downstream performance is a longstanding and very topical question in reinforcement learning. In particular, Unsupervised Environment Design (UED) methods have gained recent attention as their adaptive curricula enable agents to be robust to in- and out-of-distribution tasks. We ask to what extent these methods are themselves robust when applied to a novel setting, closely inspired by a real-world robotics problem. Surprisingly, we find that the state-of-the-art UED methods either do not improve upon the na\"{i}ve baseline of Domain Randomisation (DR), or require substantial hyperparameter tuning to do so. Our analysis shows that this is due to their underlying scoring functions failing to predict intuitive measures of ``learnability'', i.e., in finding the settings that the agent sometimes solves, but not always. Based on this, we instead directly train on levels with high learnability and find that this simple and intuitive approach outperforms UED methods and DR in several binary-outcome environments, including on our domain and the standard UED domain of Minigrid. We further introduce a new adversarial evaluation procedure for directly measuring robustness, closely mirroring the conditional value at risk (CVaR). We open-source all our code and present visualisations of final policies here: https://github.com/amacrutherford/sampling-for-learnability.