We revisit the identification of an $\varepsilon$-optimal policy in average-reward Markov Decision Processes (MDP). In such MDPs, two measures of complexity have appeared in the literature: the diameter, $D$, and the optimal bias span, $H$, which satisfy $H\leq D$. Prior work have studied the complexity of $\varepsilon$-optimal policy identification only when a generative model is available. In this case, it is known that there exists an MDP with $D \simeq H$ for which the sample complexity to output an $\varepsilon$-optimal policy is $\Omega(SAD/\varepsilon^2)$ where $S$ and $A$ are the sizes of the state and action spaces. Recently, an algorithm with a sample complexity of order $SAH/\varepsilon^2$ has been proposed, but it requires the knowledge of $H$. We first show that the sample complexity required to estimate $H$ is not bounded by any function of $S,A$ and $H$, ruling out the possibility to easily make the previous algorithm agnostic to $H$. By relying instead on a diameter estimation procedure, we propose the first algorithm for $(\varepsilon,\delta)$-PAC policy identification that does not need any form of prior knowledge on the MDP. Its sample complexity scales in $SAD/\varepsilon^2$ in the regime of small $\varepsilon$, which is near-optimal. In the online setting, our first contribution is a lower bound which implies that a sample complexity polynomial in $H$ cannot be achieved in this setting. Then, we propose an online algorithm with a sample complexity in $SAD^2/\varepsilon^2$, as well as a novel approach based on a data-dependent stopping rule that we believe is promising to further reduce this bound.

This paper presents a mixture version of the method-of-moment unsupervised lexicon classification by an incorporation of a Dirichlet process.

The lateral position of vehicles within their lane is a decisive factor for the range of vision of vehicle sensors. This, in turn, is crucial for a vehicle's ability to perceive its environment and gain a high situational awareness by processing the collected information. When aiming for increasing levels of vehicle autonomy, this situational awareness becomes more and more important. Thus, when validating an autonomous driving function the representativeness of the submicroscopic behavior such as the lateral offset has to be ensured. With simulations being an essential part of the validation of autonomous driving functions, models describing these phenomena are required. Possible applications are the enhancement of microscopic traffic simulations and the maneuver-based approach for scenario-based testing. This paper presents a two-level stochastic approach to model the lateral movement of vehicles within their lane during road-following maneuvers under homogeneous traffic conditions. A Markov model generates the coarse lateral offset profile. It is superposed with a noise model for the fine movements. Both models are set up using real-world data. The evaluation of the model shows promising qualitative and quantitative results, the potential for enhancements and extreme low computation times (10000 times faster than real time).

How do biological systems and machine learning algorithms compare in the number of samples required to show significant improvements in completing a task? We compared the learning efficiency of in vitro biological neural networks to the state-of-the-art deep reinforcement learning (RL) algorithms in a simplified simulation of the game `Pong'. Using DishBrain, a system that embodies in vitro neural networks with in silico computation using a high-density multi-electrode array, we contrasted the learning rate and the performance of these biological systems against time-matched learning from three state-of-the-art deep RL algorithms (i.e., DQN, A2C, and PPO) in the same game environment. This allowed a meaningful comparison between biological neural systems and deep RL. We find that when samples are limited to a real-world time course, even these very simple biological cultures outperformed deep RL algorithms across various game performance characteristics, implying a higher sample efficiency. Ultimately, even when tested across multiple types of information input to assess the impact of higher dimensional data input, biological neurons showcased faster learning than all deep reinforcement learning agents.

We quantify the efficiency of temporal difference (TD) learning over the direct, or Monte Carlo (MC), estimator for policy evaluation in reinforcement learning, with an emphasis on estimation of quantities related to rare events. Policy evaluation is complicated in the rare event setting by the long timescale of the event and by the need for \emph{relative accuracy} in estimates of very small values. Specifically, we focus on least-squares TD (LSTD) prediction for finite state Markov chains, and show that LSTD can achieve relative accuracy far more efficiently than MC. We prove a central limit theorem for the LSTD estimator and upper bound the \emph{relative asymptotic variance} by simple quantities characterizing the connectivity of states relative to the transition probabilities between them. Using this bound, we show that, even when both the timescale of the rare event and the relative accuracy of the MC estimator are exponentially large in the number of states, LSTD maintains a fixed level of relative accuracy with a total number of observed transitions of the Markov chain that is only \emph{polynomially} large in the number of states.

Probabilistic verification of neural networks is concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification include verifying the demographic parity fairness notion or quantifying the safety of a neural network. We present a new algorithm for the probabilistic verification of neural networks based on an algorithm for computing and iteratively refining lower and upper bounds on probabilities over the outputs of a neural network. By applying state-of-the-art bound propagation and branch and bound techniques from non-probabilistic neural network verification, our algorithm significantly outpaces existing probabilistic verification algorithms, reducing solving times for various benchmarks from the literature from tens of minutes to tens of seconds. Furthermore, our algorithm compares favourably even to dedicated algorithms for restricted subsets of probabilistic verification. We complement our empirical evaluation with a theoretical analysis, proving that our algorithm is sound and, under mildly restrictive conditions, also complete when using a suitable set of heuristics.

The Neural Network Field Theory correspondence (NNFT) is a mapping from neural network (NN) architectures into the space of statistical field theories (SFTs). The Bayesian renormalization group (BRG) is an information-theoretic coarse graining scheme that generalizes the principles of the Exact Renormalization Group (ERG) to arbitrarily parameterized probability distributions, including those of NNs. In BRG, coarse graining is performed in parameter space with respect to an information-theoretic distinguishability scale set by the Fisher information metric. In this paper, we unify NNFT and BRG to form a powerful new framework for exploring the space of NNs and SFTs, which we coin BRG-NNFT. With BRG-NNFT, NN training dynamics can be interpreted as inducing a flow in the space of SFTs from the information-theoretic `IR' $\rightarrow$ `UV'. Conversely, applying an information-shell coarse graining to the trained network's parameters induces a flow in the space of SFTs from the information-theoretic `UV' $\rightarrow$ `IR'. When the information-theoretic cutoff scale coincides with a standard momentum scale, BRG is equivalent to ERG. We demonstrate the BRG-NNFT correspondence on two analytically tractable examples. First, we construct BRG flows for trained, infinite-width NNs, of arbitrary depth, with generic activation functions. As a special case, we then restrict to architectures with a single infinitely-wide layer, scalar outputs, and generalized cos-net activations. In this case, we show that BRG coarse-graining corresponds exactly to the momentum-shell ERG flow of a free scalar SFT. Our analytic results are corroborated by a numerical experiment in which an ensemble of asymptotically wide NNs are trained and subsequently renormalized using an information-shell BRG scheme.

The goal of reinforcement learning is estimating a policy that maps states to actions and maximizes the cumulative reward of a Markov Decision Process (MDP). This is oftentimes achieved by estimating first the optimal (reward) value function (VF) associated with each state-action pair. When the MDP has an infinite horizon, the optimal VFs and policies are stationary under mild conditions. However, in finite-horizon MDPs, the VFs (hence, the policies) vary with time. This poses a challenge since the number of VFs to estimate grows not only with the size of the state-action space but also with the time horizon. This paper proposes a non-parametric low-rank stochastic algorithm to approximate the VFs of finite-horizon MDPs. First, we represent the (unknown) VFs as a multi-dimensional array, or tensor, where time is one of the dimensions. Then, we use rewards sampled from the MDP to estimate the optimal VFs. More precisely, we use the (truncated) PARAFAC decomposition to design an online low-rank algorithm that recovers the entries of the tensor of VFs. The size of the low-rank PARAFAC model grows additively with respect to each of its dimensions, rendering our approach efficient, as demonstrated via numerical experiments.

Cyber-physical system sensors emit multivariate time series (MTS) that monitor physical system processes. Such time series generally capture unknown numbers of states, each with a different duration, that correspond to specific conditions, e.g., "walking" or "running" in human-activity monitoring. Unsupervised identification of such states facilitates storage and processing in subsequent data analyses, as well as enhances result interpretability. Existing state-detection proposals face three challenges. First, they introduce substantial computational overhead, rendering them impractical in resourceconstrained or streaming settings. Second, although state-of-the-art (SOTA) proposals employ contrastive learning for representation, insufficient attention to false negatives hampers model convergence and accuracy. Third, SOTA proposals predominantly only emphasize offline non-streaming deployment, we highlight an urgent need to optimize online streaming scenarios. We propose E2Usd that enables efficient-yet-accurate unsupervised MTS state detection. E2Usd exploits a Fast Fourier Transform-based Time Series Compressor (fftCompress) and a Decomposed Dual-view Embedding Module (ddEM) that together encode input MTSs at low computational overhead. Additionally, we propose a False Negative Cancellation Contrastive Learning method (fnccLearning) to counteract the effects of false negatives and to achieve more cluster-friendly embedding spaces. To reduce computational overhead further in streaming settings, we introduce Adaptive Threshold Detection (adaTD). Comprehensive experiments with six baselines and six datasets offer evidence that E2Usd is capable of SOTA accuracy at significantly reduced computational overhead.

We present an algorithm for skill discovery from expert demonstrations. The algorithm first utilizes Large Language Models (LLMs) to propose an initial segmentation of the trajectories. Following that, a hierarchical variational inference framework incorporates the LLM-generated segmentation information to discover reusable skills by merging trajectory segments. To further control the trade-off between compression and reusability, we introduce a novel auxiliary objective based on the Minimum Description Length principle that helps guide this skill discovery process. Our results demonstrate that agents equipped with our method are able to discover skills that help accelerate learning and outperform baseline skill learning approaches on new long-horizon tasks in BabyAI, a grid world navigation environment, as well as ALFRED, a household simulation environment.