An Upper Bound of the Bias of Nadaraya-Watson Kernel Regression under Lipschitz Assumptions

The Nadaraya-Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in a number of related literature. However, Rosenblatt's analysis is only valid for infinitesimal bandwidth. In contrast, we propose in this paper an upper bound of the bias which holds for finite bandwidths. Moreover, contrarily to the classic analysis we allow for discontinuous first order derivative of the regression function, we extend our bounds for multidimensional domains and we include the knowledge of the bound of the regression function when it exists and if it is known, to obtain a tighter bound. We believe that this work has potential applications in those fields where some hard guarantees on the error are needed

Evaluation of the Handshake Turing Test for anthropomorphic Robots

Handshakes are fundamental and common greeting and parting gestures among humans. They are important in shaping first impressions as people tend to associate character traits with a person's handshake. To widen the social acceptability of robots and make a lasting first impression, a good handshaking ability is an important skill for social robots. Therefore, to test the human-likeness of a robot handshake, we propose an initial Turing-like test, primarily for the hardware interface to future AI agents. We evaluate the test on an android robot's hand to determine if it can pass for a human hand. This is an important aspect of Turing tests for motor intelligence where humans have to interact with a physical device rather than a virtual one. We also propose some modifications to the definition of a Turing test for such scenarios taking into account that a human needs to interact with a physical medium.

A Probabilistic Framework for Imitating Human Race Driver Behavior

Understanding and modeling human driver behavior is crucial for advanced vehicle development. However, unique driving styles, inconsistent behavior, and complex decision processes render it a challenging task, and existing approaches often lack variability or robustness. To approach this problem, we propose Probabilistic Modeling of Driver behavior (ProMoD), a modular framework which splits the task of driver behavior modeling into multiple modules. A global target trajectory distribution is learned with Probabilistic Movement Primitives, clothoids are utilized for local path generation, and the corresponding choice of actions is performed by a neural network. Experiments in a simulated car racing setting show considerable advantages in imitation accuracy and robustness compared to other imitation learning algorithms. The modular architecture of the proposed framework facilitates straightforward extensibility in driving line adaptation and sequencing of multiple movement primitives for future research.

MushroomRL: Simplifying Reinforcement Learning Research

MushroomRL is an open-source Python library developed to simplify the process of implementing and running Reinforcement Learning (RL) experiments. Compared to other available libraries, MushroomRL has been created with the purpose of providing a comprehensive and flexible framework to minimize the effort in implementing and testing novel RL methodologies. Indeed, the architecture of MushroomRL is built in such a way that every component of an RL problem is already provided, and most of the time users can only focus on the implementation of their own algorithms and experiments. The result is a library from which RL researchers can significantly benefit in the critical phase of the empirical analysis of their works. MushroomRL stable code, tutorials and documentation can be found at https://github.com/MushroomRL/mushroom-rl.

A Nonparametric Offpolicy Policy Gradient

Reinforcement learning (RL) algorithms still suffer from high sample complexity despite outstanding recent successes. The need for intensive interactions with the environment is especially observed in many widely popular policy gradient algorithms that perform updates using on-policy samples. The price of such inefficiency becomes evident in real-world scenarios such as interaction-driven robot learning, where the success of RL has been rather limited. We address this issue by building on the general sample efficiency of off-policy algorithms. With nonparametric regression and density estimation methods we construct a nonparametric Bellman equation in a principled manner, which allows us to obtain closed-form estimates of the value function, and to analytically express the full policy gradient. We provide a theoretical analysis of our estimate to show that it is consistent under mild smoothness assumptions and empirically show that our approach has better sample efficiency than state-of-the-art policy gradient methods.

Long-Term Visitation Value for Deep Exploration in Sparse Reward Reinforcement Learning

Reinforcement learning with sparse rewards is still an open challenge. Classic methods rely on getting feedback via extrinsic rewards to train the agent, and in situations where this occurs very rarely the agent learns slowly or cannot learn at all. Similarly, if the agent receives also rewards that create suboptimal modes of the objective function, it will likely prematurely stop exploring. More recent methods add auxiliary intrinsic rewards to encourage exploration. However, auxiliary rewards lead to a non-stationary target for the Q-function. In this paper, we present a novel approach that (1) plans exploration actions far into the future by using a long-term visitation count, and (2) decouples exploration and exploitation by learning a separate function assessing the exploration value of the actions. Contrary to existing methods which use models of reward and dynamics, our approach is off-policy and model-free. We further propose new tabular environments for benchmarking exploration in reinforcement learning. Empirical results on classic and novel benchmarks show that the proposed approach outperforms existing methods in environments with sparse rewards, especially in the presence of rewards that create suboptimal modes of the objective function. Results also suggest that our approach scales gracefully with the size of the environment. Source code is available at https://github.com/sparisi/visit-value-explore

Generalized Mean Estimation in Monte-Carlo Tree Search

We consider Monte-Carlo Tree Search (MCTS) applied to Markov Decision Processes (MDPs) and Partially Observable MDPs (POMDPs), and the well-known Upper Confidence bound for Trees (UCT) algorithm. In UCT, a tree with nodes (states) and edges (actions) is incrementally built by the expansion of nodes, and the values of nodes are updated through a backup strategy based on the average value of child nodes. However, it has been shown that with enough samples the maximum operator yields more accurate node value estimates than averaging. Instead of settling for one of these value estimates, we go a step further proposing a novel backup strategy which uses the power mean operator, which computes a value between the average and maximum value. We call our new approach Power-UCT and argue how the use of the power mean operator helps to speed up the learning in MCTS. We theoretically analyze our method providing guarantees of convergence to the optimum. Moreover, we discuss a heuristic approach to balance the greediness of backups by tuning the power mean operator according to the number of visits to each node. Finally, we empirically demonstrate the effectiveness of our method in well-known MDP and POMDP benchmarks, showing significant improvement in performance and convergence speed w.r.t. UCT.

Learning Algorithmic Solutions to Symbolic Planning Tasks with a Neural Computer

A key feature of intelligent behavior is the ability to learn abstract strategies that transfer to unfamiliar problems. Therefore, we present a novel architecture, based on memory-augmented networks, that is inspired by the von Neumann and Harvard architectures of modern computers. This architecture enables the learning of abstract algorithmic solutions via Evolution Strategies in a reinforcement learning setting. Applied to Sokoban, sliding block puzzle and robotic manipulation tasks, we show that the architecture can learn algorithmic solutions with strong generalization and abstraction: scaling to arbitrary task configurations and complexities, and being independent of both the data representation and the task domain.

HJB Optimal Feedback Control with Deep Differential Value Functions and Action Constraints

Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory from a specific starting configuration. In this paper we propose deep optimal feedback control to learn an optimal feedback policy rather than a single trajectory. By exploiting the inherent structure of the robot dynamics and strictly convex action cost, we can derive principled cost functions such that the optimal policy naturally obeys the action limits, is globally optimal and stable on the training domain given the optimal value function. The corresponding optimal value function is learned end-to-end by embedding a deep differential network in the Hamilton-Jacobi-Bellmann differential equation and minimizing the error of this equality while simultaneously decreasing the discounting from short- to far-sighted to enable the learning. Our proposed approach enables us to learn an optimal feedback control law in continuous time, that in contrast to existing approaches generates an optimal trajectory from any point in state-space without the need of replanning. The resulting approach is evaluated on non-linear systems and achieves optimal feedback control, where standard optimal control methods require frequent replanning.