Several methods exist for teaching robots, with one of the most prominent being Learning from Demonstration (LfD). Many LfD representations can be formulated as constrained optimization problems. We propose a novel convex formulation of the LfD problem represented as elastic maps, which models reproductions as a series of connected springs. Relying on the properties of strong duality and perturbation analysis of the constrained optimization problem, we create a confidence metric. Our method allows the demonstrated skill to be reproduced with varying confidence level yielding different levels of smoothness and flexibility. Our confidence-based method provides reproductions of the skill that perform better for a given set of constraints. By analyzing the constraints, our method can also remove unnecessary constraints. We validate our approach using several simulated and real-world experiments using a Jaco2 7DOF manipulator arm.

We study boosting algorithms from a new perspective. We show that the Lagrange dual problems of AdaBoost, LogitBoost and soft-margin LPBoost with generalized hinge loss are all entropy maximization problems. By looking at the dual problems of these boosting algorithms, we show that the success of boosting algorithms can be understood in terms of maintaining a better margin distribution by maximizing margins and at the same time controlling the margin variance.We also theoretically prove that, approximately, AdaBoost maximizes the average margin, instead of the minimum margin. The duality formulation also enables us to develop column generation based optimization algorithms, which are totally corrective. We show that they exhibit almost identical classification results to that of standard stage-wise additive boosting algorithms but with much faster convergence rates. Therefore fewer weak classifiers are needed to build the ensemble using our proposed optimization technique.

Abstract--For many robotic manipulation and contact tasks, it is crucial to accurately estimate uncertain object poses, for which certain geometry and sensor information are fused in some optimal fashion. Previous results for this problem primarily adopt sampling-based or end-to-end learning methods, which yet often suffer from the issues of efficiency and generalizability. In this paper, we propose a novel differentiable framework for this uncertain pose estimation during contact, so that it can be solved in an efficient and accurate manner with gradient-based solver. To achieve this, we introduce a new geometric definition that is highly adaptable and capable of providing differentiable contact Figure 1: Graphical abstracts illustrating our differentiable pose estimation features. Then we approach the problem from a bi-level perspective during contact. Left: A peg-in-hole task performed in a hole with and utilize the gradient of these contact features along with pose uncertainty along the x and y directions. Right: Visualization of differentiable optimization to efficiently solve for the uncertain the differentiable cost landscape and the gradient-based optimization pose. Several scenarios are implemented to demonstrate how the process utilizing force/torque sensor information acquired through proposed framework can improve existing methods.

We present MULTIGAIN 2.0, a major extension to the controller synthesis tool MultiGain, built on top of the probabilistic model checker PRISM. This new version extends MultiGain's multi-objective capabilities, by allowing for the formal verification and synthesis of controllers for probabilistic systems with multi-dimensional long-run average reward structures, steady-state constraints, and linear temporal logic properties. Additionally, MULTIGAIN 2.0 provides an approach for finding finite memory solutions and the capability for two- and three-dimensional visualization of Pareto curves to facilitate trade-off analysis in multi-objective scenarios

Recently, an intriguing class of non-convex optimization problems has emerged in the context of learning directed acyclic graphs (DAGs). These problems involve minimizing a given loss or score function, subject to a non-convex continuous constraint that penalizes the presence of cycles in a graph. In this work, we delve into the optimization challenges associated with this class of non-convex programs. To address these challenges, we propose a bi-level algorithm that leverages the non-convex constraint in a novel way. The outer level of the algorithm optimizes over topological orders by iteratively swapping pairs of nodes within the topological order of a DAG. A key innovation of our approach is the development of an effective method for generating a set of candidate swapping pairs for each iteration. At the inner level, given a topological order, we utilize off-the-shelf solvers that can handle linear constraints. The key advantage of our proposed algorithm is that it is guaranteed to find a local minimum or a KKT point under weaker conditions compared to previous work and finds solutions with lower scores. Extensive experiments demonstrate that our method outperforms state-of-the-art approaches in terms of achieving a better score. Additionally, our method can also be used as a post-processing algorithm to significantly improve the score of other algorithms. Code implementing the proposed method is available at https://github.com/duntrain/topo.

Predict-then-Optimize is a framework for using machine learning to perform decision-making under uncertainty. The central research question it asks is, "How can the structure of a decision-making task be used to tailor ML models for that specific task?" To this end, recent work has proposed learning task-specific loss functions that capture this underlying structure. However, current approaches make restrictive assumptions about the form of these losses and their impact on ML model behavior. These assumptions both lead to approaches with high computational cost, and when they are violated in practice, poor performance. In this paper, we propose solutions to these issues, avoiding the aforementioned assumptions and utilizing the ML model's features to increase the sample efficiency of learning loss functions. We empirically show that our method achieves state-of-the-art results in four domains from the literature, often requiring an order of magnitude fewer samples than comparable methods from past work. Moreover, our approach outperforms the best existing method by nearly 200% when the localness assumption is broken.

As the use of online platforms continues to grow across all demographics, users often express a desire to feel represented in the content. To improve representation in search results and recommendations, we introduce end-to-end diversification, ensuring that diverse content flows throughout the various stages of these systems, from retrieval to ranking. We develop, experiment, and deploy scalable diversification mechanisms in multiple production surfaces on the Pinterest platform, including Search, Related Products, and New User Homefeed, to improve the representation of different skin tones in beauty and fashion content. Diversification in production systems includes three components: identifying requests that will trigger diversification, ensuring diverse content is retrieved from the large content corpus during the retrieval stage, and finally, balancing the diversity-utility trade-off in a self-adjusting manner in the ranking stage. Our approaches, which evolved from using Strong-OR logical operator to bucketized retrieval at the retrieval stage and from greedy re-rankers to multi-objective optimization using determinantal point processes for the ranking stage, balances diversity and utility while enabling fast iterations and scalable expansion to diversification over multiple dimensions. Our experiments indicate that these approaches significantly improve diversity metrics, with a neutral to a positive impact on utility metrics and improved user satisfaction, both qualitatively and quantitatively, in production. An accessible PDF of this article is available at https://drive.google.com/file/d/1p5PkqC-sdtX19Y_IAjZCtiSxSEX1IP3q/view

Recent advances in many domains require more and more complicated experiment design. Such complicated experiments often have many parameters, which necessitate parameter tuning. Tree-structured Parzen estimator (TPE), a Bayesian optimization method, is widely used in recent parameter tuning frameworks. Despite its popularity, the roles of each control parameter and the algorithm intuition have not been discussed so far. In this tutorial, we will identify the roles of each control parameter and their impacts on hyperparameter optimization using a diverse set of benchmarks. We compare our recommended setting drawn from the ablation study with baseline methods and demonstrate that our recommended setting improves the performance of TPE.

LGPs extend GPs to a large class of settings, including noisy, categorical, and count data. However, To achieve scalable and accurate inference for LGP inference is generally analytically intractable and latent Gaussian processes, we propose a variational hence requires approximations. In addition, direct GP inference approximation based on a family of Gaussian is prohibitive for large datasets due to cubic scaling distributions whose covariance matrices have in the data size. There are two main challenges for (L)GPs sparse inverse Cholesky (SIC) factors. We combine in many applications: One is to specify or learn a suitable this variational approximation of the posterior kernel for the GP, and the other is carrying out fast inference with a similar and efficient SIC-restricted for a given kernel. In this paper, we make no contributions Kullback-Leibler-optimal approximation of the to the former and instead focus on the latter challenge: We prior. We then focus on a particular SIC ordering assume that a parametric kernel form is given and propose and nearest-neighbor-based sparsity pattern an efficient approximation method for LGP inference via resulting in highly accurate prior and posterior structured variational learning.

Hyperparameter optimization (HPO) is crucial for strong performance of deep learning algorithms and real-world applications often impose some constraints, such as memory usage, or latency on top of the performance requirement. In this work, we propose constrained TPE (c-TPE), an extension of the widely-used versatile Bayesian optimization method, tree-structured Parzen estimator (TPE), to handle these constraints. Our proposed extension goes beyond a simple combination of an existing acquisition function and the original TPE, and instead includes modifications that address issues that cause poor performance. We thoroughly analyze these modifications both empirically and theoretically, providing insights into how they effectively overcome these challenges. In the experiments, we demonstrate that c-TPE exhibits the best average rank performance among existing methods with statistical significance on 81 expensive HPO with inequality constraints. Due to the lack of baselines, we only discuss the applicability of our method to hard-constrained optimization in Appendix D.