Stable gait generation is a crucial problem for legged robot locomotion as this impacts other critical performance factors such as, e.g. mobility over an uneven terrain and power consumption. Gait generation stability results from the efficient control of the interaction between the legged robot's body and the environment where it moves. Here, we study how this can be achieved by a combination of model-predictive and predictive reinforcement learning controllers. Model-predictive control (MPC) is a well-established method that does not utilize any online learning (except for some adaptive variations) as it provides a convenient interface for state constraints management. Reinforcement learning (RL), in contrast, relies on adaptation based on pure experience. In its bare-bone variants, RL is not always suitable for robots due to their high complexity and expensive simulation/experimentation. In this work, we combine both control methods to address the quadrupedal robot stable gate generation problem. The hybrid approach that we develop and apply uses a cost roll-out algorithm with a tail cost in the form of a Q-function modeled by a neural network; this allows to alleviate the computational complexity, which grows exponentially with the prediction horizon in a purely MPC approach. We demonstrate that our RL gait controller achieves stable locomotion at short horizons, where a nominal MP controller fails. Further, our controller is capable of live operation, meaning that it does not require previous training. Our results suggest that the hybridization of MPC with RL, as presented here, is beneficial to achieve a good balance between online control capabilities and computational complexity.
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Multiscale stochastic dynamical systems have been widely adopted to scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to investigating the effective reduced dynamics for a slow-fast stochastic dynamical system. Given observation data on a short-term period satisfying some unknown slow-fast stochastic system, we propose a novel algorithm including a neural network called Auto-SDE to learn invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also proved to be accurate, stable and effective through numerical experiments under various evaluation metrics.
A novel and fully distributed optimization method is proposed for the distributed robust convex program (DRCP) over a time-varying unbalanced directed network without imposing any differentiability assumptions. Firstly, a tractable approximated DRCP (ADRCP) is introduced by discretizing the semi-infinite constraints into a finite number of inequality constraints and restricting the right-hand side of the constraints with a proper positive parameter, which will be iteratively solved by a random-fixed projection algorithm. Secondly, a cutting-surface consensus approach is proposed for locating an approximately optimal consensus solution of the DRCP with guaranteed feasibility. This approach is based on iteratively approximating the DRCP by successively reducing the restriction parameter of the right-hand constraints and populating the cutting-surfaces into the existing finite set of constraints. Thirdly, to ensure finite-time convergence of the distributed optimization, a distributed termination algorithm is developed based on uniformly local consensus and zeroth-order optimality under uniformly strongly connected graphs. Fourthly, it is proved that the cutting-surface consensus approach converges within a finite number of iterations. Finally, the effectiveness of the approach is illustrated through a numerical example.
Large machine learning models are revolutionary technologies of artificial intelligence whose bottlenecks include huge computational expenses, power, and time used both in the pre-training and fine-tuning process. In this work, we show that fault-tolerant quantum computing could possibly provide provably efficient resolutions for generic (stochastic) gradient descent algorithms, scaling as $\mathcal{O}(T^2 \times \text{polylog}(n))$, where $n$ is the size of the models and $T$ is the number of iterations in the training, as long as the models are both sufficiently dissipative and sparse, with small learning rates. Based on earlier efficient quantum algorithms for dissipative differential equations, we find and prove that similar algorithms work for (stochastic) gradient descent, the primary algorithm for machine learning. In practice, we benchmark instances of large machine learning models from 7 million to 103 million parameters. We find that, in the context of sparse training, a quantum enhancement is possible at the early stage of learning after model pruning, motivating a sparse parameter download and re-upload scheme. Our work shows solidly that fault-tolerant quantum algorithms could potentially contribute to most state-of-the-art, large-scale machine-learning problems.
Quantum computers promise exponential speed ups over classical computers for various tasks. This emerging technology is expected to have its first huge impact in High Performance Computing (HPC), as it can solve problems beyond the reach of HPC. To that end, HPC will require quantum accelerators, which will enable applications to run on both classical and quantum devices, via hybrid quantum-classical nodes. Hybrid quantum-HPC applications should be scalable, executable on Quantum Error Corrected (QEC) devices, and could use quantum-classical primitives. However, the lack of scalability, poor performances, and inability to insert classical schemes within quantum applications has prevented current quantum frameworks from being adopted by the HPC community. This paper specifies the requirements of a hybrid quantum-classical framework for HPC, and introduces a novel hardware-agnostic framework called Q-Pragma. This framework extends the classical programming language C++ heavily used in HPC via the addition of pragma directives to manage quantum computations.
We consider the problem of minimizing the makespan on batch processing identical machines, subject to compatibility constraints, where two jobs are compatible if they can be processed simultaneously in a same batch. These constraints are modeled by an undirected graph $G$, in which compatible jobs are represented by adjacent vertices. We show that several subproblems are polynomial. We propose some exact polynomial algorithms to solve these subproblems. To solve the general case, we propose a mixed-integer linear programming (MILP) formulation alongside with heuristic approaches. Furthermore, computational experiments are carried out to measure the performance of the proposed methods.
Previous researchers conducting Just-In-Time (JIT) defect prediction tasks have primarily focused on the performance of individual pre-trained models, without exploring the relationship between different pre-trained models as backbones. In this study, we build six models: RoBERTaJIT, CodeBERTJIT, BARTJIT, PLBARTJIT, GPT2JIT, and CodeGPTJIT, each with a distinct pre-trained model as its backbone. We systematically explore the differences and connections between these models. Specifically, we investigate the performance of the models when using Commit code and Commit message as inputs, as well as the relationship between training efficiency and model distribution among these six models. Additionally, we conduct an ablation experiment to explore the sensitivity of each model to inputs. Furthermore, we investigate how the models perform in zero-shot and few-shot scenarios. Our findings indicate that each model based on different backbones shows improvements, and when the backbone's pre-training model is similar, the training resources that need to be consumed are much more closer. We also observe that Commit code plays a significant role in defect detection, and different pre-trained models demonstrate better defect detection ability with a balanced dataset under few-shot scenarios. These results provide new insights for optimizing JIT defect prediction tasks using pre-trained models and highlight the factors that require more attention when constructing such models. Additionally, CodeGPTJIT and GPT2JIT achieved better performance than DeepJIT and CC2Vec on the two datasets respectively under 2000 training samples. These findings emphasize the effectiveness of transformer-based pre-trained models in JIT defect prediction tasks, especially in scenarios with limited training data.
This work considers Bayesian experimental design for the inverse boundary value problem of linear elasticity in a two-dimensional setting. The aim is to optimize the positions of compactly supported pressure activations on the boundary of the examined body in order to maximize the value of the resulting boundary deformations as data for the inverse problem of reconstructing the Lam\'e parameters inside the object. We resort to a linearized measurement model and adopt the framework of Bayesian experimental design, under the assumption that the prior and measurement noise distributions are mutually independent Gaussians. This enables the use of the standard Bayesian A-optimality criterion for deducing optimal positions for the pressure activations. The (second) derivatives of the boundary measurements with respect to the Lam\'e parameters and the positions of the boundary pressure activations are deduced to allow minimizing the corresponding objective function, i.e., the trace of the covariance matrix of the posterior distribution, by a gradient-based optimization algorithm. Two-dimensional numerical experiments are performed to demonstrate the functionality of our approach.
Bayesian binary regression is a prosperous area of research due to the computational challenges encountered by currently available methods either for high-dimensional settings or large datasets, or both. In the present work, we focus on the expectation propagation (EP) approximation of the posterior distribution in Bayesian probit regression under a multivariate Gaussian prior distribution. Adapting more general derivations in Anceschi et al. (2023), we show how to leverage results on the extended multivariate skew-normal distribution to derive an efficient implementation of the EP routine having a per-iteration cost that scales linearly in the number of covariates. This makes EP computationally feasible also in challenging high-dimensional settings, as shown in a detailed simulation study.
Swarm robotic systems utilize collective behaviour to achieve goals that might be too complex for a lone entity, but become attainable with localized communication and collective decision making. In this paper, a behaviour-based distributed approach to shape formation is proposed. Flocking into strategic formations is observed in migratory birds and fish to avoid predators and also for energy conservation. The formation is maintained throughout long periods without collapsing and is advantageous for communicating within the flock. Similar behaviour can be deployed in multi-agent systems to enhance coordination within the swarm. Existing methods for formation control are either dependent on the size and geometry of the formation or rely on maintaining the formation with a single reference in the swarm (the leader). These methods are not resilient to failure and involve a high degree of deformation upon obstacle encounter before the shape is recovered again. To improve the performance, artificial force-based interaction amongst the entities of the swarm to maintain shape integrity while encountering obstacles is elucidated.
Electrical circuits are present in a variety of technologies, making their design an important part of computer aided engineering. The growing number of tunable parameters that affect the final design leads to a need for new approaches of quantifying their impact. Machine learning may play a key role in this regard, however current approaches often make suboptimal use of existing knowledge about the system at hand. In terms of circuits, their description via modified nodal analysis is well-understood. This particular formulation leads to systems of differential-algebraic equations (DAEs) which bring with them a number of peculiarities, e.g. hidden constraints that the solution needs to fulfill. We aim to use the recently introduced dissection concept for DAEs that can decouple a given system into ordinary differential equations, only depending on differential variables, and purely algebraic equations that describe the relations between differential and algebraic variables. The idea then is to only learn the differential variables and reconstruct the algebraic ones using the relations from the decoupling. This approach guarantees that the algebraic constraints are fulfilled up to the accuracy of the nonlinear system solver, which represents the main benefit highlighted in this article.
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