Sethu Vijayakumar

Incremental Online Learning in High Dimensions

Locally weighted projection regression (LWPR) is a new algorithm for incremental nonlinear function approximation in high-dimensional spaces with redundant and irrelevant input dimensions. At its core, it employs nonparametric regression with locally linear models. In order to stay computationally efficient and numerically robust, each local model performs the regression analysis with a small number of univariate regressions in selected directions in input space in the spirit of partial least squares regression. We discuss when and how local learning techniques can successfully work in high-dimensional spaces and review the various techniques for local dimensionality reduction before finally deriving the LWPR algorithm. The properties of LWPR are that it (1) learns rapidly with second-order learning methods based on incremental training, (2) uses statistically sound stochastic leave-one-out cross validation for learning without the need to memorize training data, (3) adjusts its weighting kernels based on only local information in order to minimize the danger of negative interference of incremental learning, (4) has a computational complexity that is linear in the number of inputs, and (5) can deal with a large number ofpossibly redundantinputs, as shown in various empirical evaluations with up to 90 dimensional data sets. For a probabilistic interpretation, predictive variance and confidence intervals are derived. To our knowledge, LWPR is the first truly incremental spatially localized learning method that can successfully and efficiently operate in very high-dimensional spaces.

Natural actor-critic

This paper investigates a novel model-free reinforcement learning architecture, the Natural Actor-Critic. The actor updates are based on stochastic policy gradients employing Amaris natural gradient approach, while the critic obtains both the natural policy gradient and additional parameters of a value function simultaneously by linear regression. We show that actor improvements with natural policy gradients are particularly appealing as these are independent of coordinate frame of the chosen policy representation, and can be estimated more efficiently than regular policy gradients. The critic makes use of a special basis function parameterization motivated by the policy-gradient compatible function approximation. We show that several well-known reinforcement learning methods such as the original Actor-Critic and Bradtkes Linear Quadratic Q-Learning are in fact Natural Actor-Critic algorithms. Empirical evaluations illustrate the effectiveness of our techniques in comparison to previous methods, and also demonstrate their applicability for learning control on an anthropomorphic robot arm.

Learning inverse kinematics

Real-time control of the end-effector of a humanoid robot in external coordinates requires computationally efficient solutions of the inverse kinematics problem. In this context, this paper investigates inverse kinematics learning for resolved motion rate control (RMRC) employing an optimization criterion to resolve kinematic redundancies. Our learning approach is based on the key observations that learning an inverse of a nonuniquely invertible function can be accomplished by augmenting the input representation to the inverse model and by using a spatially localized learning approach. We apply this strategy to inverse kinematics learning and demonstrate how a recently developed statistical learning algorithm, locally weighted projection regression, allows efficient learning of inverse kinematic mappings in an incremental fashion even when input spaces become rather high dimensional. Our results are illustrated with a 30-DOF humanoid robot.

Scalable Techniques from Nonparametric Statistics for Real Time Robot Learning

Locally weighted learning (LWL) is a class of techniques from nonparametric statistics that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional belief that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested on up to 90 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing by a humanoid robot arm, and inverse-dynamics learning for a seven and a 30 degree-of-freedom robot. In all these examples, the application of our statistical neural networks techniques allowed either faster or more accurate acquisition of motor control than classical control engineering.

Hierarchical Procrustes Matching for Shape Retrieval

We introduce Hierarchical Procrustes Matching (HPM), a segment-based shape matching algorithm which avoids problems associated with purely global or local methods and performs well on benchmark shape retrieval tests. The simplicity of the shape representation leads to a powerful matching algorithm which incorporates intuitive ideas about the perceptual nature of shape while being computationally efficient. This includes the ability to match similar parts even when they occur at different scales or positions. While comparison of multiscale shape representations is typically based on specific features, HPM avoids the need to extract such features. The hierarchical structure of the algorithm captures the appealing notion that matching should proceed in a global to local direction.

The role of feed-forward and feedback processes for closed-loop prosthesis control

BackgroundIt is widely believed that both feed-forward and feed-back mechanisms are required for successful object manipulation. Open-loop upper-limb prosthesis wearers receive no tactile feedback, which may be the cause of their limited dexterity and compromised grip force control. In this paper we ask whether observed prosthesis control impairments are due to lack of feedback or due to inadequate feed-forward control.MethodsHealthy subjects were fitted with a closed-loop robotic hand and instructed to grasp and lift objects of different weights as we recorded trajectories and force profiles. We conducted three experiments under different feed-forward and feed-back configurations to elucidate the role of tactile feedback (i) in ideal conditions, (ii) under sensory deprivation, and (iii) under feed-forward uncertainty.Results(i) We found that subjects formed economical grasps in ideal conditions. (ii) To our surprise, this ability was preserved even when visual and tactile feedback were removed. (iii) When we introduced uncertainty into the hand controller performance degraded significantly in the absence of either visual or tactile feedback. Greatest performance was achieved when both sources of feedback were present.ConclusionsWe have introduced a novel method to understand the cognitive processes underlying grasping and lifting. We have shown quantitatively that tactile feedback can significantly improve performance in the presence of feed-forward uncertainty. However, our results indicate that feed-forward and feed-back mechanisms serve complementary roles, suggesting that to improve on the state-of-the-art in prosthetic hands we must develop prostheses that empower users to correct for the inevitable uncertainty in their feed-forward control.

Statistical Learning for Humanoid Robots

The complexity of the kinematic and dynamic structure of humanoid robots make conventional analytical approaches to control increasingly unsuitable for such systems. Learning techniques offer a possible way to aid controller design if insufficient analytical knowledge is available, and learning approaches seem mandatory when humanoid systems are supposed to become completely autonomous. While recent research in neural networks and statistical learning has focused mostly on learning from finite data sets without stringent constraints on computational efficiency, learning for humanoid robots requires a different setting, characterized by the need for real-time learning performance from an essentially infinite stream of incrementally arriving data. This paper demonstrates how even high-dimensional learning problems of this kind can successfully be dealt with by techniques from nonparametric regression and locally weighted learning. As an example, we describe the application of one of the most advanced of such algorithms, Locally Weighted Projection Regression (LWPR), to the on-line learning of three problems in humanoid motor control: the learning of inverse dynamics models for model-based control, the learning of inverse kinematics of redundant manipulators, and the learning of oculomotor reflexes. All these examples demonstrate fast, i.e., within seconds or minutes, learning convergence with highly accurate final peformance. We conclude that real-time learning for complex motor system like humanoid robots is possible with appropriately tailored algorithms, such that increasingly autonomous robots with massive learning abilities should be achievable in the near future.

On Stochastic Optimal Control and Reinforcement Learning by Approximate Inference

We present a reformulation of the stochastic optimal control problem in terms of KL divergence minimisation, not only providing a unifying perspective of previous approaches in this area, but also demonstrating that the formalism leads to novel practical approaches to the control problem. Specifically, a natural relaxation of the dual formulation gives rise to exact iter- ative solutions to the finite and infinite horizon stochastic optimal control problem, while direct application of Bayesian inference methods yields instances of risk sensitive control. We furthermore study corresponding formulations in the reinforcement learning setting and present model free algorithms for problems with both discrete and continuous state and action spaces. Evaluation of the proposed methods on the standard Gridworld and Cart-Pole benchmarks verifies the theoretical insights and shows that the proposed methods improve upon current approaches.

Real-time robot learning with locally weighted statistical learning

Locally weighted learning (LWL) is a class of statistical learning techniques that provides useful representations and training algorithms for learning about complex phenomena during autonomous adaptive control of robotic systems. This paper introduces several LWL algorithms that have been tested successfully in real-time learning of complex robot tasks. We discuss two major classes of LWL, memory-based LWL and purely incremental LWL that does not need to remember any data explicitly. In contrast to the traditional beliefs that LWL methods cannot work well in high-dimensional spaces, we provide new algorithms that have been tested in up to 50 dimensional learning problems. The applicability of our LWL algorithms is demonstrated in various robot learning examples, including the learning of devil-sticking, pole-balancing of a humanoid robot arm, and inverse-dynamics learning for a seven degree of-freedom robot.

Overt visual attention for a humanoid robot

The goal of our research is to investigate the interplay between oculomotor control, visual processing, and limb control in humans and primates by exploring the computational issues of these processes with a biologically inspired artificial oculomotor system on an anthropomorphic robot. In this paper, we investigate the computational mechanisms for visual attention in such a system. Stimuli in the environment excite a dynamical neural network that implements a saliency map, i.e., a winner-take-all competition between stimuli while simultaneously smoothing out noise and suppressing irrelevant inputs. In real-time, this system computes new targets for the shift of gaze, executed by the head-eye system of the robot. The redundant degrees-of-freedom of the head-eye system are resolved through a learned inverse kinematics with optimization criterion. We also address important issues how to ensure that the coordinate system of the saliency map remains correct after movement of the robot. The presented attention system is built on principled modules and generally applicable for any sensory modality.