Meta reinforcement learning (meta-RL) methods such as RL$^2$ have emerged as promising approaches for learning data-efficient RL algorithms tailored to a given task distribution. However, these RL algorithms struggle with long-horizon tasks and out-of-distribution tasks since they rely on recurrent neural networks to process the sequence of experiences instead of summarizing them into general RL components such as value functions. Moreover, even transformers have a practical limit to the length of histories they can efficiently reason about before training and inference costs become prohibitive. In contrast, traditional RL algorithms are data-inefficient since they do not leverage domain knowledge, but they do converge to an optimal policy as more data becomes available. In this paper, we propose RL$^3$, a principled hybrid approach that combines traditional RL and meta-RL by incorporating task-specific action-values learned through traditional RL as an input to the meta-RL neural network. We show that RL$^3$ earns greater cumulative reward on long-horizon and out-of-distribution tasks compared to RL$^2$, while maintaining the efficiency of the latter in the short term. Experiments are conducted on both custom and benchmark discrete domains from the meta-RL literature that exhibit a range of short-term, long-term, and complex dependencies.

Spatial perception is a key task in several machine intelligence applications such as robotics and computer vision. In general, it involves the nonlinear estimation of hidden variables that represent the system's state. However, in the presence of measurement outliers, the standard nonlinear least squared formulation results in poor estimates. Several methods have been considered in the literature to improve the reliability of the estimation process. Most methods are based on heuristics since guaranteed global robust estimation is not generally practical due to high computational costs. Recently general purpose robust estimation heuristics have been proposed that leverage existing non-minimal solvers available for the outlier-free formulations without the need for an initial guess. In this work, we propose three Bayesian heuristics that have similar structures. We evaluate these heuristics in practical scenarios to demonstrate their merits in different applications including 3D point cloud registration, mesh registration and pose graph optimization. The general computational advantages our proposals offer make them attractive candidates for spatial perception tasks.

Large-scale discrete fracture network (DFN) simulators are standard fare for studies involving the sub-surface transport of particles since direct observation of real world underground fracture networks is generally infeasible. While these simulators have seen numerous successes over several engineering applications, estimations on quantities of interest (QoI) - such as breakthrough time of particles reaching the edge of the system - suffer from a two distinct types of uncertainty. A run of a DFN simulator requires several parameter values to be set that dictate the placement and size of fractures, the density of fractures, and the overall permeability of the system; uncertainty on the proper parameter choices will lead to some amount of uncertainty in the QoI, called epistemic uncertainty. Furthermore, since DFN simulators rely on stochastic processes to place fractures and govern flow, understanding how this randomness affects the QoI requires several runs of the simulator at distinct random seeds. The uncertainty in the QoI attributed to different realizations (i.e. different seeds) of the same random process leads to a second type of uncertainty, called aleatoric uncertainty. In this paper, we perform a Sensitivity Analysis, which directly attributes the uncertainty observed in the QoI to the epistemic uncertainty from each input parameter and to the aleatoric uncertainty. We make several design choices to handle an observed heteroskedasticity in DFN simulators, where the aleatoric uncertainty changes for different inputs, since the quality makes several standard statistical methods inadmissible. Beyond the specific takeaways on which input variables affect uncertainty the most for DFN simulators, a major contribution of this paper is the introduction of a statistically rigorous workflow for characterizing the uncertainty in DFN flow simulations that exhibit heteroskedasticity.

Diffusion models are a class of flexible generative models trained with an approximation to the log-likelihood objective. However, most use cases of diffusion models are not concerned with likelihoods, but instead with downstream objectives such as human-perceived image quality or drug effectiveness. In this paper, we investigate reinforcement learning methods for directly optimizing diffusion models for such objectives. We describe how posing denoising as a multi-step decisionmaking problem enables a class of policy gradient algorithms, which we refer to as denoising diffusion policy optimization (DDPO), that are more effective than alternative reward-weighted likelihood approaches. Empirically, DDPO can adapt text-to-image diffusion models to objectives that are difficult to express via prompting, such as image compressibility, and those derived from human feedback, such as aesthetic quality. Finally, we show that DDPO can improve prompt-image alignment using feedback from a vision-language model without the need for additional data collection or human annotation. The project's website can be found at Diffusion probabilistic models (Sohl-Dickstein et al., 2015) have recently emerged as the de facto standard for generative modeling in continuous domains. The key idea behind diffusion models is to iteratively transform a simple prior distribution into a target distribution by applying a sequential denoising process. This procedure is conventionally motivated as a maximum likelihood estimation problem, with the objective derived as a variational lower bound on the log-likelihood of the training data. However, most use cases of diffusion models are not directly concerned with likelihoods, but instead with downstream objective such as human-perceived image quality or drug effectiveness.

This research introduces a novel approach, MBO-NB, that leverages Migrating Birds Optimization (MBO) coupled with Naive Bayes as an internal classifier to address feature selection challenges in text classification having large number of features. Focusing on computational efficiency, we preprocess raw data using the Information Gain algorithm, strategically reducing the feature count from an average of 62221 to 2089. Our experiments demonstrate MBO-NB's superior effectiveness in feature reduction compared to other existing techniques, emphasizing an increased classification accuracy. The successful integration of Naive Bayes within MBO presents a well-rounded solution. In individual comparisons with Particle Swarm Optimization (PSO), MBO-NB consistently outperforms by an average of 6.9% across four setups. This research offers valuable insights into enhancing feature selection methods, providing a scalable and effective solution for text classification

Sparse Bayesian Learning (SBL) models are extensively used in signal processing and machine learning for promoting sparsity through hierarchical priors. The hyperparameters in SBL models are crucial for the model's performance, but they are often difficult to estimate due to the non-convexity and the high-dimensionality of the associated objective function. This paper presents a comprehensive framework for hyperparameter estimation in SBL models, encompassing well-known algorithms such as the expectation-maximization (EM), MacKay, and convex bounding (CB) algorithms. These algorithms are cohesively interpreted within an alternating minimization and linearization (AML) paradigm, distinguished by their unique linearized surrogate functions. Additionally, a novel algorithm within the AML framework is introduced, showing enhanced efficiency, especially under low signal noise ratios. This is further improved by a new alternating minimization and quadratic approximation (AMQ) paradigm, which includes a proximal regularization term. The paper substantiates these advancements with thorough convergence analysis and numerical experiments, demonstrating the algorithm's effectiveness in various noise conditions and signal-to-noise ratios.

We provide optimal lower bounds for two well-known parameter estimation (also known as statistical estimation) tasks in high dimensions with approximate differential privacy. First, we prove that for any $\alpha \le O(1)$, estimating the covariance of a Gaussian up to spectral error $\alpha$ requires $\tilde{\Omega}\left(\frac{d^{3/2}}{\alpha \varepsilon} + \frac{d}{\alpha^2}\right)$ samples, which is tight up to logarithmic factors. This result improves over previous work which established this for $\alpha \le O\left(\frac{1}{\sqrt{d}}\right)$, and is also simpler than previous work. Next, we prove that estimating the mean of a heavy-tailed distribution with bounded $k$th moments requires $\tilde{\Omega}\left(\frac{d}{\alpha^{k/(k-1)} \varepsilon} + \frac{d}{\alpha^2}\right)$ samples. Previous work for this problem was only able to establish this lower bound against pure differential privacy, or in the special case of $k = 2$. Our techniques follow the method of fingerprinting and are generally quite simple. Our lower bound for heavy-tailed estimation is based on a black-box reduction from privately estimating identity-covariance Gaussians. Our lower bound for covariance estimation utilizes a Bayesian approach to show that, under an Inverse Wishart prior distribution for the covariance matrix, no private estimator can be accurate even in expectation, without sufficiently many samples.

We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension, conditioned on the data and previous posterior dimensions. Posterior samples are obtained by interpolating the predicted quantiles using monotonic cubic Hermite spline, with specific treatment for the tail behavior and multi-modal distributions. We introduce an alternative definition for the Bayesian credible region using the local Cumulative Density Function (CDF), offering substantially faster evaluation than the traditional Highest Posterior Density Region (HPDR). In case of limited simulation budget and/or known model misspecification, a post-processing broadening step can be integrated into NQE to ensure the unbiasedness of the posterior estimation with negligible additional computational cost. We demonstrate that the proposed NQE method achieves state-of-the-art performance on a variety of benchmark problems.

Factor Analysis based on multivariate $t$ distribution ($t$fa) is a useful robust tool for extracting common factors on heavy-tailed or contaminated data. However, $t$fa is only applicable to vector data. When $t$fa is applied to matrix data, it is common to first vectorize the matrix observations. This introduces two challenges for $t$fa: (i) the inherent matrix structure of the data is broken, and (ii) robustness may be lost, as vectorized matrix data typically results in a high data dimension, which could easily lead to the breakdown of $t$fa. To address these issues, starting from the intrinsic matrix structure of matrix data, a novel robust factor analysis model, namely bilinear factor analysis built on the matrix-variate $t$ distribution ($t$bfa), is proposed in this paper. The novelty is that it is capable to simultaneously extract common factors for both row and column variables of interest on heavy-tailed or contaminated matrix data. Two efficient algorithms for maximum likelihood estimation of $t$bfa are developed. Closed-form expression for the Fisher information matrix to calculate the accuracy of parameter estimates are derived. Empirical studies are conducted to understand the proposed $t$bfa model and compare with related competitors. The results demonstrate the superiority and practicality of $t$bfa. Importantly, $t$bfa exhibits a significantly higher breakdown point than $t$fa, making it more suitable for matrix data.

We introduce a novel sampler called the energy based diffusion generator for generating samples from arbitrary target distributions. The sampling model employs a structure similar to a variational autoencoder, utilizing a decoder to transform latent variables from a simple distribution into random variables approximating the target distribution, and we design an encoder based on the diffusion model. Leveraging the powerful modeling capacity of the diffusion model for complex distributions, we can obtain an accurate variational estimate of the Kullback-Leibler divergence between the distributions of the generated samples and the target. Moreover, we propose a decoder based on generalized Hamiltonian dynamics to further enhance sampling performance. Through empirical evaluation, we demonstrate the effectiveness of our method across various complex distribution functions, showcasing its superiority compared to existing methods.