Learning Solutions of Stochastic Optimization Problems with Bayesian Neural Networks

Mathematical solvers use parametrized Optimization Problems (OPs) as inputs to yield optimal decisions. In many real-world settings, some of these parameters are unknown or uncertain. Recent research focuses on predicting the value of these unknown parameters using available contextual features, aiming to decrease decision regret by adopting end-to-end learning approaches. However, these approaches disregard prediction uncertainty and therefore make the mathematical solver susceptible to provide erroneous decisions in case of low-confidence predictions. We propose a novel framework that models prediction uncertainty with Bayesian Neural Networks (BNNs) and propagates this uncertainty into the mathematical solver with a Stochastic Programming technique. The differentiable nature of BNNs and differentiable mathematical solvers allow for two different learning approaches: In the Decoupled learning approach, we update the BNN weights to increase the quality of the predictions' distribution of the OP parameters, while in the Combined learning approach, we update the weights aiming to directly minimize the expected OP's cost function in a stochastic end-to-end fashion. We do an extensive evaluation using synthetic data with various noise properties and a real dataset, showing that decisions regret are generally lower (better) with both proposed methods.

DataSP: A Differential All-to-All Shortest Path Algorithm for Learning Costs and Predicting Paths with Context

Learning latent costs of transitions on graphs from trajectories demonstrations under various contextual features is challenging but useful for path planning. Yet, existing methods either oversimplify cost assumptions or scale poorly with the number of observed trajectories. This paper introduces DataSP, a differentiable all-to-all shortest path algorithm to facilitate learning latent costs from trajectories. It allows to learn from a large number of trajectories in each learning step without additional computation. Complex latent cost functions from contextual features can be represented in the algorithm through a neural network approximation. We further propose a method to sample paths from DataSP in order to reconstruct/mimic observed paths' distributions. We prove that the inferred distribution follows the maximum entropy principle. We show that DataSP outperforms state-of-the-art differentiable combinatorial solver and classical machine learning approaches in predicting paths on graphs.

Learning Extrinsic Dexterity with Parameterized Manipulation Primitives

Many practically relevant robot grasping problems feature a target object for which all grasps are occluded, e.g., by the environment. Single-shot grasp planning invariably fails in such scenarios. Instead, it is necessary to first manipulate the object into a configuration that affords a grasp. We solve this problem by learning a sequence of actions that utilize the environment to change the object's pose. Concretely, we employ hierarchical reinforcement learning to combine a sequence of learned parameterized manipulation primitives. By learning the low-level manipulation policies, our approach can control the object's state through exploiting interactions between the object, the gripper, and the environment. Designing such a complex behavior analytically would be infeasible under uncontrolled conditions, as an analytic approach requires accurate physical modeling of the interaction and contact dynamics. In contrast, we learn a hierarchical policy model that operates directly on depth perception data, without the need for object detection, pose estimation, or manual design of controllers. We evaluate our approach on picking box-shaped objects of various weight, shape, and friction properties from a constrained table-top workspace. Our method transfers to a real robot and is able to successfully complete the object picking task in 98\% of experimental trials.

Heterogeneous Full-body Control of a Mobile Manipulator with Behavior Trees

Integrating the heterogeneous controllers of a complex mechanical system, such as a mobile manipulator, within the same structure and in a modular way is still challenging. In this work we extend our framework based on Behavior Trees for the control of a redundant mechanical system to the problem of commanding more complex systems that involve multiple low-level controllers. This allows the integrated systems to achieve non-trivial goals that require coordination among the sub-systems.

Towards Task-Prioritized Policy Composition

Combining learned policies in a prioritized, ordered manner is desirable because it allows for modular design and facilitates data reuse through knowledge transfer. In control theory, prioritized composition is realized by null-space control, where low-priority control actions are projected into the null-space of high-priority control actions. Such a method is currently unavailable for Reinforcement Learning. We propose a novel, task-prioritized composition framework for Reinforcement Learning, which involves a novel concept: The indifferent-space of Reinforcement Learning policies. Our framework has the potential to facilitate knowledge transfer and modular design while greatly increasing data efficiency and data reuse for Reinforcement Learning agents. Further, our approach can ensure high-priority constraint satisfaction, which makes it promising for learning in safety-critical domains like robotics. Unlike null-space control, our approach allows learning globally optimal policies for the compound task by online learning in the indifference-space of higher-level policies after initial compound policy construction.

Transferring Knowledge for Reinforcement Learning in Contact-Rich Manipulation

In manufacturing, assembly tasks have been a challenge for learning algorithms due to variant dynamics of different environments. Reinforcement learning (RL) is a promising framework to automatically learn these tasks, yet it is still not easy to apply a learned policy or skill, that is the ability of solving a task, to a similar environment even if the deployment conditions are only slightly different. In this paper, we address the challenge of transferring knowledge within a family of similar tasks by leveraging multiple skill priors. We propose to learn prior distribution over the specific skill required to accomplish each task and compose the family of skill priors to guide learning the policy for a new task by comparing the similarity between the target task and the prior ones. Our method learns a latent action space representing the skill embedding from demonstrated trajectories for each prior task. We have evaluated our method on a set of peg-in-hole insertion tasks and demonstrate better generalization to new tasks that have never been encountered during training.

A Stack-of-Tasks Approach Combined with Behavior Trees: a New Framework for Robot Control

Stack-of-Tasks (SoT) control allows a robot to simultaneously fulfill a number of prioritized goals formulated in terms of (in)equality constraints in error space. Since this approach solves a sequence of Quadratic Programs (QP) at each time-step, without taking into account any temporal state evolution, it is suitable for dealing with local disturbances. However, its limitation lies in the handling of situations that require non-quadratic objectives to achieve a specific goal, as well as situations where countering the control disturbance would require a locally suboptimal action. Recent works address this shortcoming by exploiting Finite State Machines (FSMs) to compose the tasks in such a way that the robot does not get stuck in local minima. Nevertheless, the intrinsic trade-off between reactivity and modularity that characterizes FSMs makes them impractical for defining reactive behaviors in dynamic environments. In this letter, we combine the SoT control strategy with Behavior Trees (BTs), a task switching structure that addresses some of the limitations of the FSMs in terms of reactivity, modularity and re-usability. Experimental results on a Franka Emika Panda 7-DOF manipulator show the robustness of our framework, that allows the robot to benefit from the reactivity of both SoT and BTs.

The effect of Target Normalization and Momentum on Dying ReLU

Optimizing parameters with momentum, normalizing data values, and using rectified linear units (ReLUs) are popular choices in neural network (NN) regression. Although ReLUs are popular, they can collapse to a constant function and "die", effectively removing their contribution from the model. While some mitigations are known, the underlying reasons of ReLUs dying during optimization are currently poorly understood. In this paper, we consider the effects of target normalization and momentum on dying ReLUs. We find empirically that unit variance targets are well motivated and that ReLUs die more easily, when target variance approaches zero. To further investigate this matter, we analyze a discrete-time linear autonomous system, and show theoretically how this relates to a model with a single ReLU and how common properties can result in dying ReLU. We also analyze the gradients of a single-ReLU model to identify saddle points and regions corresponding to dying ReLU and how parameters evolve into these regions when momentum is used. Finally, we show empirically that this problem persist, and is aggravated, for deeper models including residual networks.

Ensemble of Sparse Gaussian Process Experts for Implicit Surface Mapping with Streaming Data

Creating maps is an essential task in robotics and provides the basis for effective planning and navigation. In this paper, we learn a compact and continuous implicit surface map of an environment from a stream of range data with known poses. For this, we create and incrementally adjust an ensemble of approximate Gaussian process (GP) experts which are each responsible for a different part of the map. Instead of inserting all arriving data into the GP models, we greedily trade-off between model complexity and prediction error. Our algorithm therefore uses less resources on areas with few geometric features and more where the environment is rich in variety. We evaluate our approach on synthetic and real-world data sets and analyze sensitivity to parameters and measurement noise. The results show that we can learn compact and accurate implicit surface models under different conditions, with a performance comparable to or better than that of exact GP regression with subsampled data.

Multi-Object Rearrangement with Monte Carlo Tree Search:A Case Study on Planar Nonprehensile Sorting

In this work, we address a planar non-prehensile sorting task. Here, a robot needs to push many densely packed objects belonging to different classes into a configuration where these classes are clearly separated from each other. To achieve this, we propose to employ Monte Carlo tree search equipped with a task-specific heuristic function. We evaluate the algorithm on various simulated sorting tasks and observe its effectiveness in reliably sorting up to 40 convex objects. In addition, we observe that the algorithm is capable to also sort non-convex objects, as well as convex objects in the presence of immovable obstacles.