We study methods based on reproducing kernel Hilbert spaces for estimating the value function of an infinite-horizon discounted Markov reward process (MRP). We study a regularized form of the kernel least-squares temporal difference (LSTD) estimate; in the population limit of infinite data, it corresponds to the fixed point of a projected Bellman operator defined by the associated reproducing kernel Hilbert space. The estimator itself is obtained by computing the projected fixed point induced by a regularized version of the empirical operator; due to the underlying kernel structure, this reduces to solving a linear system involving kernel matrices. We analyze the error of this estimate in the $L^2(\mu)$-norm, where $\mu$ denotes the stationary distribution of the underlying Markov chain. Our analysis imposes no assumptions on the transition operator of the Markov chain, but rather only conditions on the reward function and population-level kernel LSTD solutions. We use empirical process theory techniques to derive a non-asymptotic upper bound on the error with explicit dependence on the eigenvalues of the associated kernel operator, as well as the instance-dependent variance of the Bellman residual error. In addition, we prove minimax lower bounds over sub-classes of MRPs, which shows that our rate is optimal in terms of the sample size $n$ and the effective horizon $H = (1 - \gamma)^{-1}$. Whereas existing worst-case theory predicts cubic scaling ($H^3$) in the effective horizon, our theory reveals that there is in fact a much wider range of scalings, depending on the kernel, the stationary distribution, and the variance of the Bellman residual error. Notably, it is only parametric and near-parametric problems that can ever achieve the worst-case cubic scaling.

Integer programs provide a powerful abstraction for representing a wide range of real-world scheduling problems. Despite their ability to model general scheduling problems, solving large-scale integer programs (IP) remains a computational challenge in practice. The incorporation of more complex objectives such as robustness to disruptions further exacerbates the computational challenge. We present NICE (Neural network IP Coefficient Extraction), a novel technique that combines reinforcement learning and integer programming to tackle the problem of robust scheduling. More specifically, NICE uses reinforcement learning to approximately represent complex objectives in an integer programming formulation. We use NICE to determine assignments of pilots to a flight crew schedule so as to reduce the impact of disruptions. We compare NICE with (1) a baseline integer programming formulation that produces a feasible crew schedule, and (2) a robust integer programming formulation that explicitly tries to minimize the impact of disruptions. Our experiments show that, across a variety of scenarios, NICE produces schedules resulting in 33\% to 48\% fewer disruptions than the baseline formulation. Moreover, in more severely constrained scheduling scenarios in which the robust integer program fails to produce a schedule within 90 minutes, NICE is able to build robust schedules in less than 2 seconds on average.

The framework of deep reinforcement learning (DRL) provides a powerful and widely applicable mathematical formalization for sequential decision-making. In this paper, we start from studying the f-divergence between learning policy and sampling policy and derive a novel DRL framework, termed f-Divergence Reinforcement Learning (FRL). We highlight that the policy evaluation and policy improvement phases are induced by minimizing f-divergence between learning policy and sampling policy, which is distinct from the conventional DRL algorithm objective that maximizes the expected cumulative rewards. Besides, we convert this framework to a saddle-point optimization problem with a specific f function through Fenchel conjugate, which consists of policy evaluation and policy improvement. Then we derive new policy evaluation and policy improvement methods in FRL. Our framework may give new insights for analyzing DRL algorithms. The FRL framework achieves two advantages: (1) policy evaluation and policy improvement processes are derived simultaneously by f-divergence; (2) overestimation issue of value function are alleviated. To evaluate the effectiveness of the FRL framework, we conduct experiments on Atari 2600 video games, which show that our framework matches or surpasses the DRL algorithms we tested.

An informative measurement is the most efficient way to gain information about an unknown state. We give a first-principles derivation of a general-purpose dynamic programming algorithm that returns a sequence of informative measurements by sequentially maximizing the entropy of possible measurement outcomes. This algorithm can be used by an autonomous agent or robot to decide where best to measure next, planning a path corresponding to an optimal sequence of informative measurements. This algorithm is applicable to states and controls that are continuous or discrete, and agent dynamics that is either stochastic or deterministic; including Markov decision processes. Recent results from approximate dynamic programming and reinforcement learning, including on-line approximations such as rollout and Monte Carlo tree search, allow an agent or robot to solve the measurement task in real-time. The resulting near-optimal solutions include non-myopic paths and measurement sequences that can generally outperform, sometimes substantially, commonly-used greedy heuristics such as maximizing the entropy of each measurement outcome. This is demonstrated for a global search problem, where on-line planning with an extended local search is found to reduce the number of measurements in the search by half.

In the Bayesian reinforcement learning (RL) setting, a prior distribution over the unknown problem parameters -- the rewards and transitions -- is assumed, and a policy that optimizes the (posterior) expected return is sought. A common approximation, which has been recently popularized as meta-RL, is to train the agent on a sample of $N$ problem instances from the prior, with the hope that for large enough $N$, good generalization behavior to an unseen test instance will be obtained. In this work, we study generalization in Bayesian RL under the probably approximately correct (PAC) framework, using the method of algorithmic stability. Our main contribution is showing that by adding regularization, the optimal policy becomes stable in an appropriate sense. Most stability results in the literature build on strong convexity of the regularized loss -- an approach that is not suitable for RL as Markov decision processes (MDPs) are not convex. Instead, building on recent results of fast convergence rates for mirror descent in regularized MDPs, we show that regularized MDPs satisfy a certain quadratic growth criterion, which is sufficient to establish stability. This result, which may be of independent interest, allows us to study the effect of regularization on generalization in the Bayesian RL setting.

Approximation of the value functions in value-based deep reinforcement learning systems induces overestimation bias, resulting in suboptimal policies. We show that when the reinforcement signals received by the agents have a high variance, deep actor-critic approaches that overcome the overestimation bias lead to a substantial underestimation bias. We introduce a parameter-free, novel deep Q-learning variant to reduce this underestimation bias for continuous control. By obtaining fixed weights in computing the critic objective as a linear combination of the approximate critic functions, our Q-value update rule integrates the concepts of Clipped Double Q-learning and Maxmin Q-learning. We test the performance of our improvement on a set of MuJoCo and Box2D continuous control tasks and find that it improves the state-of-the-art and outperforms the baseline algorithms in the majority of the environments.

Cooperative multi-agent reinforcement learning is a decentralized paradigm in sequential decision making where agents distributed over a network iteratively collaborate with neighbors to maximize global (network-wide) notions of rewards. Exact computations typically involve a complexity that scales exponentially with the number of agents. To address this curse of dimensionality, we design a scalable algorithm based on the Natural Policy Gradient framework that uses local information and only requires agents to communicate with neighbors within a certain range. Under standard assumptions on the spatial decay of correlations for the transition dynamics of the underlying Markov process and the localized learning policy, we show that our algorithm converges to the globally optimal policy with a dimension-free statistical and computational complexity, incurring a localization error that does not depend on the number of agents and converges to zero exponentially fast as a function of the range of communication.

The steady increase in the number of vehicles operating on the highways continues to exacerbate congestion, accidents, energy consumption, and greenhouse gas emissions. Emerging mobility systems, e.g., connected and automated vehicles (CAVs), have the potential to directly address these issues and improve transportation network efficiency and safety. In this paper, we consider a highway merging scenario and propose a framework for coordinating CAVs such that stop-and-go driving is eliminated. We use a decentralized form of the actor-critic approach to deep reinforcement learning$-$multi-agent deep deterministic policy gradient. We demonstrate the coordination of CAVs through numerical simulations and show that a smooth traffic flow is achieved by eliminating stop-and-go driving. Videos and plots of the simulation results can be found at this supplemental $\href{https://sites.google.com/view/ud-ids-lab/MADRL}{site}$.

In this paper, to reduce the congestion rate at the city center and increase the quality of experience (QoE) of each user, the framework of long-range autonomous valet parking (LAVP) is presented, where an Electric Autonomous Vehicle (EAV) is deployed in the city, which can pick up, drop off users at their required spots, and then drive to the car park out of city center autonomously. In this framework, we aim to minimize the overall distance of the EAV, while guarantee all users are served, i.e., picking up, and dropping off users at their required spots through optimizing the path planning of the EAV and number of serving time slots. To this end, we first propose a learning based algorithm, which is named as Double-Layer Ant Colony Optimization (DL-ACO) algorithm to solve the above problem in an iterative way. Then, to make the real-time decision, while consider the dynamic environment (i.e., the EAV may pick up and drop off users from different locations), we further present a deep reinforcement learning (DRL) based algorithm, which is known as deep Q network (DQN). The experimental results show that the DL-ACO and DQN-based algorithms both achieve the considerable performance.

Advanced metamorphic malware and ransomware, by using obfuscation, could alter their internal structure with every attack. If such malware could intrude even into any of the IoT networks, then even if the original malware instance gets detected, by that time it can still infect the entire network. It is challenging to obtain training data for such evasive malware. Therefore, in this paper, we present ADVERSARIALuscator, a novel system that uses specialized Adversarial-DRL to obfuscate malware at the opcode level and create multiple metamorphic instances of the same. To the best of our knowledge, ADVERSARIALuscator is the first-ever system that adopts the Markov Decision Process-based approach to convert and find a solution to the problem of creating individual obfuscations at the opcode level. This is important as the machine language level is the least at which functionality could be preserved so as to mimic an actual attack effectively. ADVERSARIALuscator is also the first-ever system to use efficient continuous action control capable of deep reinforcement learning agents like the Proximal Policy Optimization in the area of cyber security. Experimental results indicate that ADVERSARIALuscator could raise the metamorphic probability of a corpus of malware by >0.45. Additionally, more than 33% of metamorphic instances generated by ADVERSARIALuscator were able to evade the most potent IDS. If such malware could intrude even into any of the IoT networks, then even if the original malware instance gets detected, by that time it can still infect the entire network. Hence ADVERSARIALuscator could be used to generate data representative of a swarm of very potent and coordinated AI-based metamorphic malware attacks. The so generated data and simulations could be used to bolster the defenses of an IDS against an actual AI-based metamorphic attack from advanced malware and ransomware.