In recent years, a myriad of advanced results have been reported in the community of imitation learning, ranging from parametric to non-parametric, probabilistic to non-probabilistic and Bayesian to frequentist approaches. Meanwhile, ample applications (e.g., grasping tasks and human-robot collaborations) further show the applicability of imitation learning in a wide range of domains. While numerous literature is dedicated to the learning of human skills in unconstrained environment, the problem of learning constrained motor skills, however, has not received equal attention yet. In fact, constrained skills exist widely in robotic systems. For instance, when a robot is demanded to write letters on a board, its end-effector trajectory must comply with the plane constraint from the board. In this paper, we aim to tackle the problem of imitation learning with linear constraints. Specifically, we propose to exploit the probabilistic properties of multiple demonstrations, and subsequently incorporate them into a linearly constrained optimization problem, which finally leads to a non-parametric solution. In addition, a connection between our framework and the classical model predictive control is provided. Several examples including simulated writing and locomotion tasks are presented to show the effectiveness of our framework.

An algorithm is an unambiguous rule of action to solve a problem or a class of problems. Algorithms consist of a finite number of well-defined individual steps. Thus, they can be implemented in a computer program for execution, but can also be formulated in human language. When solving a problem, a specific input is converted into a particular output. In the following, five algorithms are listed that have significantly influenced our world.

An algorithm is an unambiguous rule of action to solve a problem or a class of problems. Algorithms consist of a finite number of well-defined individual steps. Thus, they can be implemented in a computer program for execution, but can also be formulated in human language. When solving a problem, a specific input is converted into a particular output. In the following, five algorithms are listed that have significantly influenced our world.

In this paper, we propose a communication- and computation-efficient algorithm to solve a convex consensus optimization problem defined over a decentralized network. A remarkable existing algorithm to solve this problem is the alternating direction method of multipliers (ADMM), in which at every iteration every node updates its local variable through combining neighboring variables and solving an optimization subproblem. The proposed algorithm, called as COmmunication-censored Linearized ADMM (COLA), leverages a linearization technique to reduce the iteration-wise computation cost of ADMM and uses a communication-censoring strategy to alleviate the communication cost. To be specific, COLA introduces successive linearization approximations to the local cost functions such that the resultant computation is first-order and light-weight. Since the linearization technique slows down the convergence speed, COLA further adopts the communication-censoring strategy to avoid transmissions of less informative messages. A node is allowed to transmit only if the distance between the current local variable and its previously transmitted one is larger than a censoring threshold. COLA is proven to be convergent when the local cost functions have Lipschitz continuous gradients and the censoring threshold is summable. When the local cost functions are further strongly convex, we establish the linear (sublinear) convergence rate of COLA, given that the censoring threshold linearly (sublinearly) decays to 0. Numerical experiments corroborate with the theoretical findings and demonstrate the satisfactory communication-computation tradeoff of COLA.

Distributed Pseudo-tree Optimization Procedure (DPOP) is a well-known message passing algorithm that has been used to provide optimal solutions of Distributed Constraint Optimization Problems (DCOPs) -- a framework that is designed to optimize constraints in cooperative multi-agent systems. The traditional DCOP formulation does not consider those constraints that must be satisfied (also known as hard constraints), rather it concentrates only on soft constraints. However, the presence of both types of constraints are observed in a number of applications, such as Distributed Radio Link Frequency Assignment and Distributed Event Scheduling, etc. Although the combination of these types of constraints is recently incorporated in DPOP to solve DCOPs, scalability remains an issue for them as finding an optimal solution is NP-hard. Additionally, in DPOP, the agents are arranged as a DFS pseudo-tree. Recently it has been observed that the constructed pseudo-trees in this way often come to be chain-like and greatly impair the algorithm's performance. To address these issues, we develop an algorithm that speeds up the DPOP algorithm by reducing the size of the messages exchanged and increasing parallelism in the pseudo tree. Our empirical evidence suggests that our approach outperforms the state-of-the-art algorithms by a significant margin.

Structural optimization is a popular method for designing objects such as bridge trusses, airplane wings, and optical devices. Unfortunately, the quality of solutions depends heavily on how the problem is parameterized. In this paper, we propose using the implicit bias over functions induced by neural networks to improve the parameterization of structural optimization. Rather than directly optimizing densities on a grid, we instead optimize the parameters of a neural network which outputs those densities. This reparameterization leads to different and often better solutions. On a selection of 116 structural optimization tasks, our approach produces the best design 50% more often than the best baseline method.

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.

WASHINGTON, D.C. – Today, the U.S. Department of Energy's (DOE's) Advanced Research Projects Agency-Energy (ARPA-E) announced up to $20 million in funding to accelerate the incorporation of machine learning and artificial intelligence into energy technology and product design processes. The Design Intelligence for Formidable Energy Reduction Engendering Numerous Totally Impactful Advanced Technology Enhancements (DIFFERENTIATE) program seeks to enhance energy innovation by incorporating artificial intelligence and machine learning into energy technology development. "Artificial intelligence and machine learning has the potential to literally transform every aspect of the world as we know it, and accelerating this technology is crucial to strengthening our country's economic and national security," said U.S. Secretary of Energy Rick Perry. "DOE-fueled artificial intelligence is being utilized across all sectors, from strengthening cybersecurity and national security, increasing energy efficiency, optimizing grid security and resiliency, and developing innovative health solutions. The DIFFERENTIATE program is the latest example of DOE paving the way towards the New American Energy Era." In order to organize these efforts, DIFFERNTIATE identifies six general mathematical optimization problems that are common to many design processes. It then conceptualizes several machine learning tools that could help engineers execute and solve these problems in a manner that dramatically accelerates the pace of energy innovation.

Programming-by-Example (PBE) systems synthesize an intended program in some (relatively constrained) domain-specific language from a small number of input-output examples provided by the user. In this paper, we motivate and define the problem of quantitative PBE (qPBE) that relates to synthesizing an intended program over an underlying (real world) programming language that also minimizes a given quantitative cost function. We present a modular approach for solving qPBE that consists of three phases: intent disambiguation, global search, and local search. On two concrete objectives, namely program performance and size, our qPBE procedure achieves $1.53 X$ and $1.26 X$ improvement respectively over the baseline FlashFill PBE system, averaged over $701$ benchmarks. Our detailed experiments validate the design of our procedure and show the value of combining global and local search for qPBE.

Population-based memetic algorithms have been successfully applied to solve many difficult combinatorial problems. Often, a population of fixed size was used in such algorithms to record some best solutions sampled during the search. However, given the particular features of the problem instance under consideration, a population of variable size would be more suitable to ensure the best search performance possible. In this work, we propose variable population memetic search (VPMS), where a strategic population sizing mechanism is used to dynamically adjust the population size during the memetic search process. Our VPMS approach starts its search from a small population of only two solutions to focus on exploitation, and then adapts the population size according to the search status to continuously influence the balancing between exploitation and exploration. We illustrate an application of the VPMS approach to solve the challenging critical node problem (CNP). We show that the VPMS algorithm integrating a variable population, an effective local optimization procedure (called diversified late acceptance search) and a backbone-based crossover operator performs very well compared to state-of-the-art CNP algorithms. The algorithm is able to discover new upper bounds for 13 instances out of the 42 popular benchmark instances, while matching 23 previous best-known upper bounds.