Data generation and labeling are often expensive in robot learning. Preference-based learning is a concept that enables reliable labeling by querying users with preference questions. Active querying methods are commonly employed in preference-based learning to generate more informative data at the expense of parallelization and computation time. In this paper, we develop a set of novel algorithms, batch active preference-based learning methods, that enable efficient learning of reward functions using as few data samples as possible while still having short query generation times and also retaining parallelizability. We introduce a method based on determinantal point processes (DPP) for active batch generation and several heuristic-based alternatives. Finally, we present our experimental results for a variety of robotics tasks in simulation. Our results suggest that our batch active learning algorithm requires only a few queries that are computed in a short amount of time. We showcase one of our algorithms in a study to learn human users' preferences.

Diffusion models are powerful generative models but suffer from slow sampling, often taking 1000 sequential denoising steps for one sample. As a result, considerable efforts have been directed toward reducing the number of denoising steps, but these methods hurt sample quality. Instead of reducing the number of denoising steps (trading quality for speed), in this paper we explore an orthogonal approach: can we run the denoising steps in parallel (trading compute for speed)? In spite of the sequential nature of the denoising steps, we show that surprisingly it is possible to parallelize sampling via Picard iterations, by guessing the solution of future denoising steps and iteratively refining until convergence. With this insight, we present ParaDiGMS, a novel method to accelerate the sampling of pretrained diffusion models by denoising multiple steps in parallel. ParaDiGMS is the first diffusion sampling method that enables trading compute for speed and is even compatible with existing fast sampling techniques such as DDIM and DPM-Solver. Using ParaDiGMS, we improve sampling speed by 2-4x across a range of robotics and image generation models, giving state-of-the-art sampling speeds of 0.2s on 100-step DiffusionPolicy and 14.6s on 1000-step StableDiffusion-v2 with no measurable degradation of task reward, FID score, or CLIP score.

Learning from human feedback has shown to be a useful approach in acquiring robot reward functions. However, expert feedback is often assumed to be drawn from an underlying unimodal reward function. This assumption does not always hold including in settings where multiple experts provide data or when a single expert provides data for different tasks -- we thus go beyond learning a unimodal reward and focus on learning a multimodal reward function. We formulate the multimodal reward learning as a mixture learning problem and develop a novel ranking-based learning approach, where the experts are only required to rank a given set of trajectories. Furthermore, as access to interaction data is often expensive in robotics, we develop an active querying approach to accelerate the learning process. We conduct experiments and user studies using a multi-task variant of OpenAI's LunarLander and a real Fetch robot, where we collect data from multiple users with different preferences. The results suggest that our approach can efficiently learn multimodal reward functions, and improve data-efficiency over benchmark methods that we adapt to our learning problem.

Determinantal point processes (DPPs) are widely popular probabilistic models used in machine learning to capture diversity in random subsets of items. While traditional DPPs are defined by a symmetric kernel matrix, recent work has shown a significant increase in the modeling power and applicability of models defined by nonsymmetric kernels, where the model can capture interactions that go beyond diversity. We study the problem of maximum a posteriori (MAP) inference for determinantal point processes defined by a nonsymmetric positive semidefinite matrix (NDPPs), where the goal is to find the maximum $k\times k$ principal minor of the kernel matrix $L$. We obtain the first multiplicative approximation guarantee for this problem using local search, a method that has been previously applied to symmetric DPPs. Our approximation factor of $k^{O(k)}$ is nearly tight, and we show theoretically and experimentally that it compares favorably to the state-of-the-art methods for this problem that are based on greedy maximization. The main new insight enabling our improved approximation factor is that we allow local search to update up to two elements of the solution in each iteration, and we show this is necessary to have any multiplicative approximation guarantee.

In this paper we provide a new efficient algorithm for approximately computing the profile maximum likelihood (PML) distribution, a prominent quantity in symmetric property estimation. We provide an algorithm which matches the previous best known efficient algorithms for computing approximate PML distributions and improves when the number of distinct observed frequencies in the given instance is small. We achieve this result by exploiting new sparsity structure in approximate PML distributions and providing a new matrix rounding algorithm, of independent interest. Leveraging this result, we obtain the first provable computationally efficient implementation of PseudoPML, a general framework for estimating a broad class of symmetric properties. Additionally, we obtain efficient PML-based estimators for distributions with small profile entropy, a natural instance-based complexity measure. Further, we provide a simpler and more practical PseudoPML implementation that matches the best-known theoretical guarantees of such an estimator and evaluate this method empirically.

Data collection and labeling is one of the main challenges in employing machine learning algorithms in a variety of real-world applications with limited data. While active learning methods attempt to tackle this issue by labeling only the data samples that give high information, they generally suffer from large computational costs and are impractical in settings where data can be collected in parallel. Batch active learning methods attempt to overcome this computational burden by querying batches of samples at a time. To avoid redundancy between samples, previous works rely on some ad hoc combination of sample quality and diversity. In this paper, we present a new principled batch active learning method using Determinantal Point Processes, a repulsive point process that enables generating diverse batches of samples. We develop tractable algorithms to approximate the mode of a DPP distribution, and provide theoretical guarantees on the degree of approximation. We further demonstrate that an iterative greedy method for DPP maximization, which has lower computational costs but worse theoretical guarantees, still gives competitive results for batch active learning. Our experiments show the value of our methods on several datasets against state-of-the-art baselines.

We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon [BCMV14] but allows for a wider range of perturbation models, including discrete ones. We give an application to recovering assemblies of neurons. Assemblies are large sets of neurons representing specific memories or concepts. The size of the intersection of two assemblies has been shown in experiments to represent the extent to which these memories co-occur or these concepts are related; the phenomenon is called association of assemblies. This suggests that an animal's memory is a complex web of associations, and poses the problem of recovering this representation from cognitive data. Motivated by this problem, we study the following more general question: Can we reconstruct the Venn diagram of a family of sets, given the sizes of their l-wise intersections? We show that as long as the family of sets is randomly perturbed, it is enough for the number of measurements to be polynomially larger than the number of nonempty regions of the Venn diagram to fully reconstruct the diagram.

We analyze linear independence of rank one tensors produced by tensor powers of randomly perturbed vectors. This enables efficient decomposition of sums of high-order tensors. Our analysis builds upon [BCMV14] but allows for a wider range of perturbation models, including discrete ones. We give an application to recovering assemblies of neurons. Assemblies are large sets of neurons representing specific memories or concepts. The size of the intersection of two assemblies has been shown in experiments to represent the extent to which these memories co-occur or these concepts are related; the phenomenon is called association of assemblies. This suggests that an animal's memory is a complex web of associations, and poses the problem of recovering this representation from cognitive data. Motivated by this problem, we study the following more general question: Can we reconstruct the Venn diagram of a family of sets, given the sizes of their l-wise intersections? We show that as long as the family of sets is randomly perturbed, it is enough for the number of measurements to be polynomially larger than the number of nonempty regions of the Venn diagram to fully reconstruct the diagram.