We investigate the problem of best policy identification in discounted linear Markov Decision Processes in the fixed confidence setting under a generative model. We first derive an instance-specific lower bound on the expected number of samples required to identify an $\varepsilon$-optimal policy with probability $1-\delta$. The lower bound characterizes the optimal sampling rule as the solution of an intricate non-convex optimization program, but can be used as the starting point to devise simple and near-optimal sampling rules and algorithms. We devise such algorithms. One of these exhibits a sample complexity upper bounded by ${\cal O}({\frac{d}{(\varepsilon+\Delta)^2}} (\log(\frac{1}{\delta})+d))$ where $\Delta$ denotes the minimum reward gap of sub-optimal actions and $d$ is the dimension of the feature space. This upper bound holds in the moderate-confidence regime (i.e., for all $\delta$), and matches existing minimax and gap-dependent lower bounds. We extend our algorithm to episodic linear MDPs.

The space of value functions is a fundamental concept in reinforcement learning. Characterizing its geometric properties may provide insights for optimization and representation. Existing works mainly focus on the value space for Markov Decision Processes (MDPs). In this paper, we study the geometry of the robust value space for the more general Robust MDPs (RMDPs) setting, where transition uncertainties are considered. Specifically, since we find it hard to directly adapt prior approaches to RMDPs, we start with revisiting the non-robust case, and introduce a new perspective that enables us to characterize both the non-robust and robust value space in a similar fashion. The key of this perspective is to decompose the value space, in a state-wise manner, into unions of hypersurfaces. Through our analysis, we show that the robust value space is determined by a set of conic hypersurfaces, each of which contains the robust values of all policies that agree on one state. Furthermore, we find that taking only extreme points in the uncertainty set is sufficient to determine the robust value space. Finally, we discuss some other aspects about the robust value space, including its non-convexity and policy agreement on multiple states.

Consider $K$ processes, each generating a sequence of identical and independent random variables. The probability measures of these processes have random parameters that must be estimated. Specifically, they share a parameter $\theta$ common to all probability measures. Additionally, each process $i\in\{1, \dots, K\}$ has a private parameter $\alpha_i$. The objective is to design an active sampling algorithm for sequentially estimating these parameters in order to form reliable estimates for all shared and private parameters with the fewest number of samples. This sampling algorithm has three key components: (i)~data-driven sampling decisions, which dynamically over time specifies which of the $K$ processes should be selected for sampling; (ii)~stopping time for the process, which specifies when the accumulated data is sufficient to form reliable estimates and terminate the sampling process; and (iii)~estimators for all shared and private parameters. Owing to the sequential estimation being known to be analytically intractable, this paper adopts \emph {conditional} estimation cost functions, leading to a sequential estimation approach that was recently shown to render tractable analysis. Asymptotically optimal decision rules (sampling, stopping, and estimation) are delineated, and numerical experiments are provided to compare the efficacy and quality of the proposed procedure with those of the relevant approaches.

We present local mappings that relate the marginal probabilities of a global probability mass function represented by its primal normal factor graph to the corresponding marginal probabilities in its dual normal factor graph. The mapping is based on the Fourier transform of the local factors of the models. Details of the mapping are provided for the Ising model, where it is proved that the local extrema of the fixed points are attained at the phase transition of the two-dimensional nearest-neighbor Ising model. The results are further extended to the Potts model, to the clock model, and to Gaussian Markov random fields. By employing the mapping, we can transform simultaneously all the estimated marginal probabilities from the dual domain to the primal domain (and vice versa), which is advantageous if estimating the marginals can be carried out more efficiently in the dual domain. An example of particular significance is the ferromagnetic Ising model in a positive external magnetic field. For this model, there exists a rapidly mixing Markov chain (called the subgraphs--world process) to generate configurations in the dual normal factor graph of the model. Our numerical experiments illustrate that the proposed procedure can provide more accurate estimates of marginal probabilities of a global probability mass function in various settings.

Malicious software (malware) causes much harm to our devices and life. We are eager to understand the malware behavior and the threat it made. Most of the record files of malware are variable length and text-based files with time stamps, such as event log data and dynamic analysis profiles. Using the time stamps, we can sort such data into sequence-based data for the following analysis. However, dealing with the text-based sequences with variable lengths is difficult. In addition, unlike natural language text data, most sequential data in information security have specific properties and structure, such as loop, repeated call, noise, etc. To deeply analyze the API call sequences with their structure, we use graphs to represent the sequences, which can further investigate the information and structure, such as the Markov model. Therefore, we design and implement an Attention Aware Graph Neural Network (AWGCN) to analyze the API call sequences. Through AWGCN, we can obtain the sequence embeddings to analyze the behavior of the malware. Moreover, the classification experiment result shows that AWGCN outperforms other classifiers in the call-like datasets, and the embedding can further improve the classic model's performance.

Most reinforcement learning (RL) recommendation systems designed for edge computing must either synchronize during recommendation selection or depend on an unprincipled patchwork collection of algorithms. In this work, we build on asynchronous coagent policy gradient algorithms \citep{kostas2020asynchronous} to propose a principled solution to this problem. The class of algorithms that we propose can be distributed over the internet and run asynchronously and in real-time. When a given edge fails to respond to a request for data with sufficient speed, this is not a problem; the algorithm is designed to function and learn in the edge setting, and network issues are part of this setting. The result is a principled, theoretically grounded RL algorithm designed to be distributed in and learn in this asynchronous environment. In this work, we describe this algorithm and a proposed class of architectures in detail, and demonstrate that they work well in practice in the asynchronous setting, even as the network quality degrades.

Recent years have seen a great increase in the capacity and parallel processing power of data centers and cloud services. To fully utilize the said distributed systems, optimal load balancing for parallel queuing architectures must be realized. Existing state-of-the-art solutions fail to consider the effect of communication delays on the behaviour of very large systems with many clients. In this work, we consider a multi-agent load balancing system, with delayed information, consisting of many clients (load balancers) and many parallel queues. In order to obtain a tractable solution, we model this system as a mean-field control problem with enlarged state-action space in discrete time through exact discretization. Subsequently, we apply policy gradient reinforcement learning algorithms to find an optimal load balancing solution. Here, the discrete-time system model incorporates a synchronization delay under which the queue state information is synchronously broadcasted and updated at all clients. We then provide theoretical performance guarantees for our methodology in large systems. Finally, using experiments, we prove that our approach is not only scalable but also shows good performance when compared to the state-of-the-art power-of-d variant of the Join-the-Shortest-Queue (JSQ) and other policies in the presence of synchronization delays.

Traffic simulation has gained a lot of interest for quantitative evaluation of self driving vehicles performance. In order for a simulator to be a valuable test bench, it is required that the driving policy animating each traffic agent in the scene acts as humans would do while maintaining minimal safety guarantees. Learning the driving policies of traffic agents from recorded human driving data or through reinforcement learning seems to be an attractive solution for the generation of realistic and highly interactive traffic situations in uncontrolled intersections or roundabouts. In this work, we show that a trade-off exists between imitating human driving and maintaining safety when learning driving policies. We do this by comparing how various Imitation learning and Reinforcement learning algorithms perform when applied to the driving task. We also propose a multi objective learning algorithm (MOPPO) that improves both objectives together. We test our driving policies on highly interactive driving scenarios extracted from INTERACTION Dataset to evaluate how human-like they behave.

We consider a class of restless bandit problems that finds a broad application area in stochastic optimization, reinforcement learning and operations research. We consider $N$ independent discrete-time Markov processes, each of which had two possible states: 1 and 0 (`good' and `bad'). Only if a process is both in state 1 and observed to be so does reward accrue. The aim is to maximize the expected discounted sum of returns over the infinite horizon subject to a constraint that only $M$ $(

Abstract-- The visual analytics community has proposed several user modeling algorithms to capture and analyze users' interaction behavior in order to assist users in data exploration and insight generation. For example, some can detect exploration biases while others can predict data points that the user will interact with before that interaction occurs. Researchers believe this collection of algorithms can help create more intelligent visual analytics tools. However, the community lacks a rigorous evaluation and comparison of these existing techniques. As a result, there is limited guidance on which method to use and when. Our paper seeks to fill in this missing gap by comparing and ranking eight user modeling algorithms based on their performance on a diverse set of four user study datasets. We analyze exploration bias detection, data interaction prediction, and algorithmic complexity, among other measures. Based on our findings, we highlight open challenges and new directions for analyzing user interactions and visualization provenance. After surveying the body of work, we selected seven proposed Researchers in the visualization community have long viewed interaction techniques and standardized their input and output specifications to as an analytic discourse between the analyst and the visualization account for a variety of datasets. In addition to the selected models, system [40].