We consider large-scale Markov decision processes with an unknown cost function and address the problem of learning a policy from a finite set of expert demonstrations. We assume that the learner is not allowed to interact with the expert and has no access to reinforcement signal of any kind. Existing inverse reinforcement learning methods come with strong theoretical guarantees, but are computationally expensive, while state-of-the-art policy optimization algorithms achieve significant empirical success, but are hampered by limited theoretical understanding. To bridge the gap between theory and practice, we introduce a novel bilinear saddle-point framework using Lagrangian duality. The proposed primal-dual viewpoint allows us to develop a model-free provably efficient algorithm through the lens of stochastic convex optimization. The method enjoys the advantages of simplicity of implementation, low memory requirements, and computational and sample complexities independent of the number of states. We further present an equivalent no-regret online-learning interpretation.

A fundamental challenge in interactive learning and decision making, ranging from bandit problems to reinforcement learning, is to provide sample-efficient, adaptive learning algorithms that achieve near-optimal regret. This question is analogous to the classical problem of optimal (supervised) statistical learning, where there are well-known complexity measures (e.g., VC dimension and Rademacher complexity) that govern the statistical complexity of learning. However, characterizing the statistical complexity of interactive learning is substantially more challenging due to the adaptive nature of the problem. The main result of this work provides a complexity measure, the Decision-Estimation Coefficient, that is proven to be both necessary and sufficient for sample-efficient interactive learning. In particular, we provide: 1. a lower bound on the optimal regret for any interactive decision making problem, establishing the Decision-Estimation Coefficient as a fundamental limit. 2. a unified algorithm design principle, Estimation-to-Decisions (E2D), which transforms any algorithm for supervised estimation into an online algorithm for decision making. E2D attains a regret bound matching our lower bound, thereby achieving optimal sample-efficient learning as characterized by the Decision-Estimation Coefficient. Taken together, these results constitute a theory of learnability for interactive decision making. When applied to reinforcement learning settings, the Decision-Estimation Coefficient recovers essentially all existing hardness results and lower bounds. More broadly, the approach can be viewed as a decision-theoretic analogue of the classical Le Cam theory of statistical estimation; it also unifies a number of existing approaches -- both Bayesian and frequentist.

The field of artificial intelligence (AI) is devoted to the creation of artificial decision-makers that can perform (at least) on par with the human counterparts on a domain of interest. Unlike the agents in traditional AI, the agents in artificial general intelligence (AGI) are required to replicate human intelligence in almost every domain of interest. Moreover, an AGI agent should be able to achieve this without (virtually any) further changes, retraining, or fine-tuning of the parameters. The real world is non-stationary, non-ergodic, and non-Markovian: we, humans, can neither revisit our past nor are the most recent observations sufficient statistics. Yet, we excel at a variety of complex tasks. Many of these tasks require longterm planning. We can associate this success to our natural faculty to abstract away task-irrelevant information from our overwhelming sensory experience. We make task-specific mental models of the world without much effort. Due to this ability to abstract, we can plan on a significantly compact representation of a task without much loss of performance. Not only this, we also abstract our actions to produce high-level plans: the level of action-abstraction can be anywhere between small muscle movements to a mental notion of "doing an action". It is natural to assume that any AGI agent competing with humans (at every plausible domain) should also have these abilities to abstract its experiences and actions. This thesis is an inquiry into the existence of such abstractions which aid efficient planing for a wide range of domains, and most importantly, these abstractions come with some optimality guarantees.

The field of General Reinforcement Learning (GRL) formulates the problem of sequential decision-making from ground up. The history of interaction constitutes a "ground" state of the system, which never repeats. On the one hand, this generality allows GRL to model almost every domain possible, e.g.\ Bandits, MDPs, POMDPs, PSRs, and history-based environments. On the other hand, in general, the near-optimal policies in GRL are functions of complete history, which hinders not only learning but also planning in GRL. The usual way around for the planning part is that the agent is given a Markovian abstraction of the underlying process. So, it can use any MDP planning algorithm to find a near-optimal policy. The Extreme State Aggregation (ESA) framework has extended this idea to non-Markovian abstractions without compromising on the possibility of planning through a (surrogate) MDP. A distinguishing feature of ESA is that it proves an upper bound of $O\left(\varepsilon^{-A} \cdot (1-\gamma)^{-2A}\right)$ on the number of states required for the surrogate MDP (where $A$ is the number of actions, $\gamma$ is the discount-factor, and $\varepsilon$ is the optimality-gap) which holds \emph{uniformly} for \emph{all} domains. While the possibility of a universal bound is quite remarkable, we show that this bound is very loose. We propose a novel non-MDP abstraction which allows for a much better upper bound of $O\left(\varepsilon^{-1} \cdot (1-\gamma)^{-2} \cdot A \cdot 2^{A}\right)$. Furthermore, we show that this bound can be improved further to $O\left(\varepsilon^{-1} \cdot (1-\gamma)^{-2} \cdot \log^3 A \right)$ by using an action-sequentialization method.

That the sequential structure of genomes is important has been known since the discovery of DNA. In this paper we employ a statistics and stochastic process perspective on triplets of successive bases to address two important applications: identifying outliers in genome databases, and classifying reads in the metagenomic context of reference-guided assembly. From this stochastic process perspective, triplets are a second-order Markov chain specified by the distribution of each base conditional on its two immediate predecessors. To be sure, studying genomes via base sequence distributions is not novel. Previous papers have addressed genome signatures (Karlin et al., 1997; Campbell et al., 1999; Takashi et al., 2003), as well as frequentist (Rosen et al., 2008) and Bayesian (Wang et al., 2007) approaches to classification problems.

We study stochastic approximation procedures for approximately solving a $d$-dimensional linear fixed point equation based on observing a trajectory of length $n$ from an ergodic Markov chain. We first exhibit a non-asymptotic bound of the order $t_{\mathrm{mix}} \tfrac{d}{n}$ on the squared error of the last iterate of a standard scheme, where $t_{\mathrm{mix}}$ is a mixing time. We then prove a non-asymptotic instance-dependent bound on a suitably averaged sequence of iterates, with a leading term that matches the local asymptotic minimax limit, including sharp dependence on the parameters $(d, t_{\mathrm{mix}})$ in the higher order terms. We complement these upper bounds with a non-asymptotic minimax lower bound that establishes the instance-optimality of the averaged SA estimator. We derive corollaries of these results for policy evaluation with Markov noise -- covering the TD($\lambda$) family of algorithms for all $\lambda \in [0, 1)$ -- and linear autoregressive models. Our instance-dependent characterizations open the door to the design of fine-grained model selection procedures for hyperparameter tuning (e.g., choosing the value of $\lambda$ when running the TD($\lambda$) algorithm).

We investigate partially observed Markov decision processes (POMDPs) with cost functions regularized by entropy terms describing state, observation, and control uncertainty. Standard POMDP techniques are shown to offer bounded-error solutions to these entropy-regularized POMDPs, with exact solutions when the regularization involves the joint entropy of the state, observation, and control trajectories. Our joint-entropy result is particularly surprising since it constitutes a novel, tractable formulation of active state estimation. Partially observed Markov decision processes (POMDPs) and Markov decision processes (MDPs) with information-theoretic costs have attracted widespread attention across the technical disciplines of systems and control [2]-[5], computer science [6]-[8], signal processing [9]-[12], and robotics [13]-[15]. Interest in such POMDPs has been driven, in large part, by active state estimation problems in which informationtheoretic costs describing the uncertainty about latent states are minimized in order to aid or enhance the performance of state estimation algorithms [5], [6], [9], [10].

Deep reinforcement learning is actively used for training autonomous driving agents in a vision-based urban simulated environment. Due to the large availability of various reinforcement learning algorithms, we are still unsure of which one works better while training autonomous cars in single-agent as well as multi-agent driving environments. A comparison of deep reinforcement learning in vision-based autonomous driving will open up the possibilities for training better autonomous car policies. Also, autonomous cars trained on deep reinforcement learning-based algorithms are known for being vulnerable to adversarial attacks, and we have less information on which algorithms would act as a good adversarial agent. In this work, we provide a systematic evaluation and comparative analysis of 6 deep reinforcement learning algorithms for autonomous and adversarial driving in four-way intersection scenario. Specifically, we first train autonomous cars using state-of-the-art deep reinforcement learning algorithms. Second, we test driving capabilities of the trained autonomous policies in single-agent as well as multi-agent scenarios. Lastly, we use the same deep reinforcement learning algorithms to train adversarial driving agents, in order to test the driving performance of autonomous cars and look for possible collision and offroad driving scenarios. We perform experiments by using vision-only high fidelity urban driving simulated environments.

Deep reinforcement learning is widely used to train autonomous cars in a simulated environment. Still, autonomous cars are well known for being vulnerable when exposed to adversarial attacks. This raises the question of whether we can train the adversary as a driving agent for finding failure scenarios in autonomous cars, and then retrain autonomous cars with new adversarial inputs to improve their robustness. In this work, we first train and compare adversarial car policy on two custom reward functions to test the driving control decision of autonomous cars in a multi-agent setting. Second, we verify that adversarial examples can be used not only for finding unwanted autonomous driving behavior, but also for helping autonomous driving cars in improving their deep reinforcement learning policies. By using a high fidelity urban driving simulation environment and vision-based driving agents, we demonstrate that the autonomous cars retrained using the adversary player noticeably increase the performance of their driving policies in terms of reducing collision and offroad steering errors.

Many experimental works have observed that generalization in deep RL appears to be difficult: although RL agents can learn to perform very complex tasks, they don't seem to generalize over diverse task distributions as well as the excellent generalization of supervised deep nets might lead us to expect. In this blog post, we will aim to explain why generalization in RL is fundamentally harder, and indeed more difficult even in theory. We will show that attempting to generalize in RL induces implicit partial observability, even when the RL problem we are trying to solve is a standard fully-observed MDP. This induced partial observability can significantly complicate the types of policies needed to generalize well, potentially requiring counterintuitive strategies like information-gathering actions, recurrent non-Markovian behavior, or randomized strategies. Ordinarily, this is not necessary in fully observed MDPs but surprisingly becomes necessary when we consider generalization from a finite training set in a fully observed MDP.