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).

Engineering problems that are modeled using sophisticated mathematical methods or are characterized by expensive-to-conduct tests or experiments, are encumbered with limited budget or finite computational resources. Moreover, practical scenarios in the industry, impose restrictions, based on logistics and preference, on the manner in which the experiments can be conducted. For example, material supply may enable only a handful of experiments in a single-shot or in the case of computational models one may face significant wait-time based on shared computational resources. In such scenarios, one usually resorts to performing experiments in a manner that allows for maximizing one's state-of-knowledge while satisfying the above mentioned practical constraints. Sequential design of experiments (SDOE) is a popular suite of methods, that has yielded promising results in recent years across different engineering and practical problems. A common strategy, that leverages Bayesian formalism is the Bayesian SDOE, which usually works best in the one-step-ahead or myopic scenario of selecting a single experiment at each step of a sequence of experiments. In this work, we aim to extend the SDOE strategy, to query the experiment or computer code at a batch of inputs. To this end, we leverage deep reinforcement learning (RL) based policy gradient methods, to propose batches of queries that are selected taking into account entire budget in hand. The algorithm retains the sequential nature, inherent in the SDOE, while incorporating elements of reward based on task from the domain of deep RL. A unique capability of the proposed methodology is its ability to be applied to multiple tasks, for example optimization of a function, once its trained. We demonstrate the performance of the proposed algorithm on a synthetic problem, and a challenging high-dimensional engineering problem.

Due to the complexity and volatility of the traffic environment, decision-making in autonomous driving is a significantly hard problem. In this project, we use a Deep Q-Network, along with rule-based constraints to make lane-changing decision. A safe and efficient lane change behavior may be obtained by combining high-level lateral decision-making with low-level rule-based trajectory monitoring. The agent is anticipated to perform appropriate lane-change maneuvers in a real-world-like udacity simulator after training it for a total of 100 episodes. The results shows that the rule-based DQN performs better than the DQN method. The rule-based DQN achieves a safety rate of 0.8 and average speed of 47 MPH

Graph walking based on reinforcement learning (RL) has shown great success in navigating an agent to automatically complete various reasoning tasks over an incomplete knowledge graph (KG) by exploring multi-hop relational paths. However, existing multi-hop reasoning approaches only work well on short reasoning paths and tend to miss the target entity with the increasing path length. This is undesirable for many reason-ing tasks in real-world scenarios, where short paths connecting the source and target entities are not available in incomplete KGs, and thus the reasoning performances drop drastically unless the agent is able to seek out more clues from longer paths. To address the above challenge, in this paper, we propose a dual-agent reinforcement learning framework, which trains two agents (GIANT and DWARF) to walk over a KG jointly and search for the answer collaboratively. Our approach tackles the reasoning challenge in long paths by assigning one of the agents (GIANT) searching on cluster-level paths quickly and providing stage-wise hints for another agent (DWARF). Finally, experimental results on several KG reasoning benchmarks show that our approach can search answers more accurately and efficiently, and outperforms existing RL-based methods for long path queries by a large margin.

Multi-agent reinforcement learning (MARL) enables us to create adaptive agents in challenging environments, even when the agents have limited observation. Modern MARL methods have hitherto focused on finding factorized value functions. While this approach has proven successful, the resulting methods have convoluted network structures. We take a radically different approach, and build on the structure of independent Q-learners. Inspired by influence-based abstraction, we start from the observation that compact representations of the observation-action histories can be sufficient to learn close to optimal decentralized policies. Combining this observation with a dueling architecture, our algorithm, LAN, represents these policies as separate individual advantage functions w.r.t. a centralized critic. These local advantage networks condition only on a single agent's local observation-action history. The centralized value function conditions on the agents' representations as well as the full state of the environment. The value function, which is cast aside before execution, serves as a stabilizer that coordinates the learning and to formulate DQN targets during learning. In contrast with other methods, this enables LAN to keep the number of network parameters of its centralized network independent in the number of agents, without imposing additional constraints like monotonic value functions. When evaluated on the StarCraft multi-agent challenge benchmark, LAN shows state-of-the-art performance and scores more than 80% wins in two previously unsolved maps `corridor' and `3s5z_vs_3s6z', leading to an improvement of 10% over QPLEX on average performance on the 14 maps. Moreover when the number of agents becomes large, LAN uses significantly fewer parameters than QPLEX or even QMIX. We thus show that LAN's structure forms a key improvement that helps MARL methods remain scalable.

In reinforcement learning, continuous time is often discretized by a time scale $\delta$, to which the resulting performance is known to be highly sensitive. In this work, we seek to find a $\delta$-invariant algorithm for policy gradient (PG) methods, which performs well regardless of the value of $\delta$. We first identify the underlying reasons that cause PG methods to fail as $\delta \to 0$, proving that the variance of the PG estimator can diverge to infinity in stochastic environments under a certain assumption of stochasticity. While durative actions or action repetition can be employed to have $\delta$-invariance, previous action repetition methods cannot immediately react to unexpected situations in stochastic environments. We thus propose a novel $\delta$-invariant method named Safe Action Repetition (SAR) applicable to any existing PG algorithm. SAR can handle the stochasticity of environments by adaptively reacting to changes in states during action repetition. We empirically show that our method is not only $\delta$-invariant but also robust to stochasticity, outperforming previous $\delta$-invariant approaches on eight MuJoCo environments with both deterministic and stochastic settings. Our code is available at https://vision.snu.ac.kr/projects/sar.

Standard single-step models have a horizon of one. This post describes a method for training predictive dynamics models in continuous state spaces with an infinite, probabilistic horizon. Reinforcement learning algorithms are frequently categorized by whether they predict future states at any point in their decision-making process. Those that do are called model-based, and those that do not are dubbed model-free. This classification is so common that we mostly take it for granted these days; I am guilty of using it myself.

In this paper, we describe two sets of experiments with small groups of real robots, conducted over the course of more than 10 years, in the Bristol Robotics Lab. The long-term aim of these ongoing experiments is to explore aspects of the question'how do we have culture?' in a new way, by modelling the low-level processes and mechanisms of cultural evolution with robots. In this paper we adopt Mesoudi's definition of culture: 'information that is acquired from other individuals via social transmission mechanisms such as imitation, teaching or language' [1]. We outline two sets of experiments--the first already completed and the second in preparation--with a focus on two of these transmission mechanisms: imitation and language. The first set of experiments we describe were directly inspired by the thought experiment in [2, p. 106], which imagines a group of robots capable of imitating each other. Referred to as Copybots, their ability to imitate actions with variation makes them very simple meme machines. Another source of inspiration was Gabriel Tarde who proposed'a remarkable sociological research project' [3] when he wrote If we wish to make sociology a truly experimental science and stamp it with the seal of exactness, we must, I believe … write out with the greatest care and in the greatest possible detail the succession of minute transformations in the political or industrial world, or some other sphere of life, … in (our) native town or village, beginning in (our) own immediate surroundings (quoted in [3, p. 511]). A second and more recent set of experiments extends our robots' cognitive capabilities with simulation-based internal models. A simulation-based internal model (literally a robot with a simulation of itself, inside itself), allows a robot to be able to ask itself'what if' questions. This capability has been described as a functional imagination [4], as it enables a robot to'imagine' the consequences of its actions (and--in our implementation--the reaction of others to those actions). Our experimental implementation of a simulation-based internal model, which we refer to as a consequence engine (CE), has proven to be remarkably powerful. Our experiments with the CE were inspired by both the simulation theory of cognition [5,6] and Dennett's'Tower of Generate-and-Test' [7].

AI Summer uses the information you provide to send you our newsletter and contact you about our products.

We train an agent to compete in the game of Gardner minichess, a downsized variation of chess played on a 5x5 board. We motivated and applied a SOTA actor-critic method Proximal Policy Optimization with Generalized Advantage Estimation. Our initial task centered around training the agent against a random agent. Once we obtained reasonable performance, we then adopted a version of iterative policy improvement adopted by AlphaGo to pit the agent against increasingly stronger versions of itself, and evaluate the resulting performance gain. The final agent achieves a near (.97) perfect win rate against a random agent. We also explore the effects of pretraining the network using a collection of positions obtained via self-play.