We address the problem of robotic grasping of known and unknown objects using implicit behavior cloning. We train a grasp evaluation model from a small number of demonstrations that outputs higher values for grasp candidates that are more likely to succeed in grasping. This evaluation model serves as an objective function, that we maximize to identify successful grasps. Key to our approach is the utilization of learned implicit representations of visual and geometric features derived from a pre-trained NeRF. Though trained exclusively in a simulated environment with simplified objects and 4-DoF top-down grasps, our evaluation model and optimization procedure demonstrate generalization to 6-DoF grasps and novel objects both in simulation and in real-world settings, without the need for additional data. Supplementary material is available at: https://gergely-soti.github.io/grasp

The distributed optimization problem has become increasingly relevant recently. It has a lot of advantages such as processing a large amount of data in less time compared to non-distributed methods. However, most distributed approaches suffer from a significant bottleneck - the cost of communications. Therefore, a large amount of research has recently been directed at solving this problem. One such approach uses local data similarity. In particular, there exists an algorithm provably optimally exploiting the similarity property. But this result, as well as results from other works solve the communication bottleneck by focusing only on the fact that communication is significantly more expensive than local computing and does not take into account the various capacities of network devices and the different relationship between communication time and local computing expenses. We consider this setup and the objective of this study is to achieve an optimal ratio of distributed data between the server and local machines for any costs of communications and local computations. The running times of the network are compared between uniform and optimal distributions. The superior theoretical performance of our solutions is experimentally validated.

Bearing measurements,as the most common modality in nature, have recently gained traction in multi-robot systems to enhance mutual localization and swarm collaboration. Despite their advantages, challenges such as sensory noise, obstacle occlusion, and uncoordinated swarm motion persist in real-world scenarios, potentially leading to erroneous state estimation and undermining the system's flexibility, practicality, and robustness.In response to these challenges, in this paper we address theoretical and practical problem related to both mutual localization and swarm planning.Firstly, we propose a certifiable mutual localization algorithm.It features a concise problem formulation coupled with lossless convex relaxation, enabling independence from initial values and globally optimal relative pose recovery.Then, to explore how detection noise and swarm motion influence estimation optimality, we conduct a comprehensive analysis on the interplay between robots' mutual spatial relationship and mutual localization. We develop a differentiable metric correlated with swarm trajectories to explicitly evaluate the noise resistance of optimal estimation.By establishing a finite and pre-computable threshold for this metric and accordingly generating swarm trajectories, the estimation optimality can be strictly guaranteed under arbitrary noise. Based on these findings, an optimization-based swarm planner is proposed to generate safe and smooth trajectories, with consideration of both inter-robot visibility and estimation optimality.Through numerical simulations, we evaluate the optimality and certifiablity of our estimator, and underscore the significance of our planner in enhancing estimation performance.The results exhibit considerable potential of our methods to pave the way for advanced closed-loop intelligence in swarm systems.

In this paper, we study the performance of federated learning over wireless networks, where devices with a limited energy budget train a machine learning model. The federated learning performance depends on the selection of the clients participating in the learning at each round. Most existing studies suggest deterministic approaches for the client selection, resulting in challenging optimization problems that are usually solved using heuristics, and therefore without guarantees on the quality of the final solution. We formulate a new probabilistic approach to jointly select clients and allocate power optimally so that the expected number of participating clients is maximized. To solve the problem, a new alternating algorithm is proposed, where at each step, the closed-form solutions for user selection probabilities and power allocations are obtained. Our numerical results show that the proposed approach achieves a significant performance in terms of energy consumption, completion time and accuracy as compared to the studied benchmarks.

In this paper, we present a novel framework for data redundancy measurement based on probabilistic modeling of datasets, and a new criterion for redundancy detection that is resilient to noise. We also develop new methods for data redundancy reduction using both deterministic and stochastic optimization techniques. Our framework is flexible and can handle different types of features, and our experiments on benchmark datasets demonstrate the effectiveness of our methods. We provide a new perspective on feature selection, and propose effective and robust approaches for both supervised and unsupervised learning problems.

For many data-intensive tasks, feature selection is an important preprocessing step. However, most existing methods do not directly and intuitively explore the intrinsic discriminative information of features. We propose a novel feature selection framework based on the distance between class conditional distributions, measured by integral probability metrics (IPMs). Our framework directly explores the discriminative information of features in the sense of distributions for supervised classification. We analyze the theoretical and practical aspects of IPMs for feature selection, construct criteria based on IPMs. We propose several variant feature selection methods of our framework based on the 1-Wasserstein distance and implement them on real datasets from different domains. Experimental results show that our framework can outperform state-of-the-art methods in terms of classification accuracy and robustness to perturbations.

Policy gradient methods hold great potential for solving complex continuous control tasks. Still, their training efficiency can be improved by exploiting structure within the optimization problem. Recent work indicates that supervised learning can be accelerated by leveraging the fact that gradients lie in a low-dimensional and slowly-changing subspace. In this paper, we conduct a thorough evaluation of this phenomenon for two popular deep policy gradient methods on various simulated benchmark tasks. Our results demonstrate the existence of such gradient subspaces despite the continuously changing data distribution inherent to reinforcement learning. These findings reveal promising directions for future work on more efficient reinforcement learning, e.g., through improving parameter-space exploration or enabling second-order optimization.

The bin packing is a well-known NP-Hard problem in the domain of artificial intelligence, posing significant challenges in finding efficient solutions. Conversely, recent advancements in quantum technologies have shown promising potential for achieving substantial computational speedup, particularly in certain problem classes, such as combinatorial optimization. In this study, we introduce QAL-BP, a novel Quadratic Unconstrained Binary Optimization (QUBO) formulation designed specifically for bin packing and suitable for quantum computation. QAL-BP utilizes the Augmented Lagrangian method to incorporate the bin packing constraints into the objective function while also facilitating an analytical estimation of heuristic, but empirically robust, penalty multipliers. This approach leads to a more versatile and generalizable model that eliminates the need for empirically calculating instance-dependent Lagrangian coefficients, a requirement commonly encountered in alternative QUBO formulations for similar problems. To assess the effectiveness of our proposed approach, we conduct experiments on a set of bin packing instances using a real Quantum Annealing device. Additionally, we compare the results with those obtained from two different classical solvers, namely simulated annealing and Gurobi. The experimental findings not only confirm the correctness of the proposed formulation, but also demonstrate the potential of quantum computation in effectively solving the bin packing problem, particularly as more reliable quantum technology becomes available.

Global optimization of decision trees has shown to be promising in terms of accuracy, size, and consequently human comprehensibility. However, many of the methods used rely on general-purpose solvers for which scalability remains an issue. Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems. However, this only works when an objective can be optimized separately for subtrees. We explore this relationship in detail and show the necessary and sufficient conditions for such separability and generalize previous dynamic programming approaches into a framework that can optimize any combination of separable objectives and constraints. Experiments on five application domains show the general applicability of this framework, while outperforming the scalability of general-purpose solvers by a large margin.

Sampling-based Model Predictive Control (MPC) has been a practical and effective approach in many domains, notably model-based reinforcement learning, thanks to its flexibility and parallelizability. Despite its appealing empirical performance, the theoretical understanding, particularly in terms of convergence analysis and hyperparameter tuning, remains absent. In this paper, we characterize the convergence property of a widely used sampling-based MPC method, Model Predictive Path Integral Control (MPPI). We show that MPPI enjoys at least linear convergence rates when the optimization is quadratic, which covers time-varying LQR systems. We then extend to more general nonlinear systems. Our theoretical analysis directly leads to a novel sampling-based MPC algorithm, CoVariance-Optimal MPC (CoVO-MPC) that optimally schedules the sampling covariance to optimize the convergence rate. Empirically, CoVO-MPC significantly outperforms standard MPPI by 43-54% in both simulations and real-world quadrotor agile control tasks.