Model-free deep reinforcement learning (RL) algorithms have achieved tremendous success on a range of challenging tasks. However, safety concerns remain when these methods are deployed on real-world applications, necessitating risk-aware agents. A common utility for learning such risk-aware agents is the entropic risk measure, but current policy gradient methods optimizing this measure must perform high-variance and numerically unstable updates. As a result, existing risk-sensitive model-free approaches are limited to simple tasks and tabular settings. In this paper, we provide a comprehensive theoretical justification for policy gradient methods on the entropic risk measure, including on- and off-policy gradient theorems for the stochastic and deterministic policy settings. Motivated by theory, we propose risk-sensitive exponential actor-critic (rsEAC), an off-policy model-free approach that incorporates novel procedures to avoid the explicit representation of exponential value functions and their gradients, and optimizes its policy w.r.t. the entropic risk measure. In this way, we show that rsEAC produces more numerically stable updates compared to existing approaches and reliably learns risk-sensitive policies in challenging risky variants of continuous tasks in MuJoCo.

Risk-sensitive reinforcement learning (RL) with an entropic risk measure typically requires knowledge of the transition kernel or performs unstable updates w.r.t. exponential Bellman equations. As a consequence, algorithms that optimize this objective have been restricted to tabular or low-dimensional continuous environments. In this work we leverage the connection between the entropic risk measure and the RL-as-inference framework to develop a risk-sensitive variational actor-critic algorithm (rsVAC). Our work extends the variational framework to incorporate stochastic rewards and proposes a variational model-based actor-critic approach that modulates policy risk via a risk parameter. We consider, both, the risk-seeking and risk-averse regimes and present rsVAC learning variants for each setting. Our experiments demonstrate that this approach produces risk-sensitive policies and yields improvements in both tabular and risk-aware variants of complex continuous control tasks in MuJoCo.

Mutual Information (MI) is a fundamental measure of dependence between random variables, but its practical application is limited because it is difficult to calculate in many circumstances. Variational methods offer one approach by introducing an approximate distribution to create various bounds on MI, which in turn is an easier optimization problem to solve. In practice, the variational distribution chosen is often a Gaussian, which is convenient but lacks flexibility in modeling complicated distributions. In this paper, we introduce new classes of variational estimators based on Normalizing Flows that extend the previous Gaussian-based variational estimators. Our new estimators maintain many of the same theoretical guarantees while simultaneously enhancing the expressivity of the variational distribution. We experimentally verify that our new methods are effective on large MI problems where discriminative-based estimators, such as MINE and InfoNCE, are fundamentally limited. Furthermore, we compare against a diverse set of benchmarking tests to show that the flow-based estimators often perform as well, if not better, than the discriminative-based counterparts. Finally, we demonstrate how these estimators can be effectively utilized in the Bayesian Optimal Experimental Design setting for online sequential decision making.

Expected information gain (EIG) is a crucial quantity in Bayesian optimal experimental design (BOED), quantifying how useful an experiment is by the amount we expect the posterior to differ from the prior. However, evaluating the EIG can be computationally expensive since it generally requires estimating the posterior normalizing constant. In this work, we leverage two idiosyncrasies of BOED to improve efficiency of EIG estimation via sequential Monte Carlo (SMC). First, in BOED we simulate the data and thus know the true underlying parameters. Second, we ultimately care about the EIG, not the individual normalizing constants. Often we observe that the Monte Carlo variance of standard SMC estimators for the normalizing constant of a single dataset are significantly lower than the variance of the normalizing constants across datasets; the latter thus contributes the majority of the variance for EIG estimates. This suggests the potential to slightly increase variance while drastically decreasing computation time by reducing the SMC population size, which leads us to an EIG-specific SMC estimator that starts with a only a single sample from the posterior and tempers \textit{backwards} towards the prior. Using this single-sample estimator, which we call reverse-annealed SMC (RA-SMC), we show that it is possible to estimate EIG with orders of magnitude fewer likelihood evaluations in three models: a four-dimensional spring-mass, a six-dimensional Johnson-Cook model and a four-dimensional source-finding problem.

Deep learning (DL)-based malware detectors have shown promise in swiftly detecting unseen malware without expensive dynamic malware behavior analysis. These detectors have been shown to be susceptible to adversarial malware variants generated from meticulously modifying known malware to mislead detectors into recognizing them as benign. Being able to automatically generate optimized functional adversarial malware variants by defenders is crucial to effective cyber defense and staying ahead of the adversary. Current adversarial malware example generation methods often assume threat models with any of the following four restrictions: (1) requiring access to insider knowledge about malware detectors, (2) an unlimited size of adversarial modifications, (3) an unlimited number of queries to malware detector, and (4) relying on dynamic analysis of malware behavior in a sandbox. Drawing on Actor-Critic Reinforcement Learning (RL), we propose a novel closed-box binary manipulation method for adversarial malware optimization, named Actor-Critic with Contextualized Action Representations (AC-CAR), to generate malware variants without these restrictions. AC-CAR leverages two novel components, a contextualized policy and a neural language model-based RL-augmented top-$k$sampling method. Unlike current methods, AC-CAR can utilize tens of thousands of actions to augment malware executables for evading DL-based malware detectors. AC-CAR yields an approximately 2-fold performance increase over the current methods on average, while decreasing the payload size to 20 times smaller than leading methods. We show that using the malware variants generated by AC-CAR in an adversarial re-training procedure improves malware detector’ robustness against adversarial variants by 29.65% on average.

We develop a family of fast variational methods for sequential control in dynamic settings where an agent is incentivized to maximize information gain. We consider the case of optimal control in continuous nonlinear dynamical systems that prohibit exact evaluation of the mutual information (MI) reward. Our approach couples efficient message-passing inference with variational bounds on the MI objective under Gaussian projections. We also develop a Gaussian mixture approximation that enables exact MI evaluation under constraints on the component covariances. We validate our methodology in nonlinear systems with superior and faster control compared to standard particle-based methods. We show our approach improves the accuracy and efficiency of one-shot robotic learning with intrinsic MI rewards. Furthermore, we demonstrate that our method is applicable to a wider range of contexts, e.g., the active information acquisition problem.

Differentially private stochastic gradient descent (DP-SGD) has been instrumental in privately training deep learning models by providing a framework to control and track the privacy loss incurred during training. At the core of this computation lies a subsampling method that uses a privacy amplification lemma to enhance the privacy guarantees provided by the additive noise. Fixed size subsampling is appealing for its constant memory usage, unlike the variable sized minibatches in Poisson subsampling. It is also of interest in addressing class imbalance and federated learning. Current computable guarantees for fixed-size subsampling are not tight and do not consider both add/remove and replace-one adjacency relationships. We present a new and holistic Rényi differential privacy (RDP) accountant for DP-SGD with fixed-size subsampling without replacement (FSwoR) and with replacement (FSwR). For FSwoR we consider both add/remove and replace-one adjacency, where we improve on the best current computable bound by a factor of $4$. We also show for the first time that the widely-used Poisson subsampling and FSwoR with replace-one adjacency have the same privacy to leading order in the sampling probability. Our work suggests that FSwoR is often preferable to Poisson subsampling due to constant memory usage. Our FSwR accountant includes explicit non-asymptotic upper and lower bounds and, to the authors' knowledge, is the first such RDP analysis of fixed-size subsampling with replacement for DP-SGD. We analytically and empirically compare fixed size and Poisson subsampling, and show that DP-SGD gradients in a fixed-size subsampling regime exhibit lower variance in practice in addition to memory usage benefits.

Computing mutual information (MI) of random variables lacks a closed-form in nontrivial models. Variational MI approximations are widely used as flexible estimators for this purpose, but computing them typically requires solving a costly nonconvex optimization. We prove that a widely used class of variational MI estimators can be solved via moment matching operations in place of the numerical optimization methods that are typically required. We show that the same moment matching solution yields variational estimates for so-called “implicit” models that lack a closed form likelihood function. Furthermore, we demonstrate that this moment matching solution has multiple orders of magnitude computational speed up compared to the standard optimization based solutions. We show that theoretical results are supported by numerical evaluation in fully parameterized Gaussian mixture models and a generalized linear model with implicit likelihood due to nuisance variables. We also demonstrate on the implicit simulation-based likelihood SIR epidemiology model, where we avoid costly likelihood free inference and observe many orders of magnitude speedup.

Gaussian mixture models (GMMs) are fundamental to machine learning due to their flexibility as approximating densities. However, uncertainty quantification of GMMs remains a challenge as differential entropy lacks a closed form. This paper explores polynomial approximations, specifically Taylor and Legendre, to the GMM entropy from a theoretical and practical perspective. We provide new analysis of a widely used approach due to Huber et al.(2008) and show that the series diverges under simple conditions. Motivated by this divergence we provide a novel Taylor series that is provably convergent to the true entropy of any GMM. We demonstrate a method for selecting a center such that the series converges from below, providing a lower bound on GMM entropy. Furthermore, we demonstrate that orthogonal polynomial series result in more accurate polynomial approximations. Experimental validation supports our theoretical results while showing that our method is comparable in computation to Huber et al. We also show that in application, the use of these polynomial approximations, such as in Nonparametric Variational Inference by Gershamn et al. (2012), rely on the convergence of the methods in computing accurate approximations. This work contributes useful analysis to existing methods while introducing a novel approximation supported by firm theoretical guarantees.

Articulated motion analysis often utilizes strong prior knowledge such as a known or trained parts model for humans. Yet, the world contains a variety of articulating objects--mammals, insects, mechanized structures--where the number and configuration of parts for a particular object is unknown in advance. Here, we relax such strong assumptions via an unsupervised, Bayesian nonparametric parts model that infers an unknown number of parts with motions coupled by a body dynamic and parameterized by SE(D), the Lie group of rigid transformations. We derive an inference procedure that utilizes short observation sequences (image, depth, point cloud or mesh) of an object in motion without need for markers or learned body models. Efficient Gibbs decompositions for inference over distributions on SE(D) demonstrate robust part decompositions of moving objects under both 3D and 2D observation models. The inferred representation permits novel analysis, such as object segmentation by relative part motion, and transfers to new observations of the same object type.

Mutual information (MI) is a commonly adopted utility function in Bayesian optimal experimental design (BOED). While theoretically appealing, MI evaluation poses a significant computational burden for most real world applications. As a result, many algorithms utilize MI bounds as proxies that lack regret-style guarantees. Here, we utilize two-sided bounds to provide such guarantees. Bounds are successively refined/tightened through additional computation until a desired guarantee is achieved. We consider the problem of adaptively allocating computational resources in BOED. Our approach achieves the same guarantee as existing methods, but with fewer evaluations of the costly MI reward. We adapt knapsack optimization of best arm identification problems, with important differences that impact overall algorithm design and performance. First, observations of MI rewards are biased. Second, evaluating experiments incurs shared costs amongst all experiments (posterior sampling) in addition to per experiment costs that may vary with increasing evaluation. We propose and demonstrate an algorithm that accounts for these variable costs in the refinement decision.

We consider the setting of sequential decision making where, at each stage, potential actions are evaluated based on expected reduction in posterior uncertainty, given by mutual information (MI). As MI typically lacks a closed form, we propose an approach which maintains variational approximations of, both, the posterior and MI utility. Our planning objective extends an established variational bound on MI to the setting of sequential planning. The result, variational information planning (VIP), is an efficient method for sequential decision making. We further establish convexity of the variational planning objective and, under conditional exponential family approximations, we show that the optimal MI bound arises from a relaxation of the well-known exponential family moment matching property. We demonstrate VIP for sensor selection, experiment design, and active learning, where it meets or exceeds methods requiring more computation, or those specialized to the task.

In many sequential planning applications a natural approach to generating high quality plans is to maximize an information reward such as mutual information (MI). Unfortunately, MI lacks a closed form in all but trivial models, and so must be estimated. In applications where the cost of plan execution is expensive, one desires planning estimates which admit theoretical guarantees. Through the use of robust M-estimators we obtain bounds on absolute deviation of estimated MI. Moreover, we propose a sequential algorithm which integrates inference and planning by maximally reusing particles in each stage. We validate the utility of using robust estimators in the sequential approach on a Gaussian Markov Random Field wherein information measures have a closed form. Lastly, we demonstrate the benefits of our integrated approach in the context of sequential experiment design for inferring causal regulatory networks from gene expression levels. Our method shows improvements over a recent method which selects intervention experiments based on the same MI objective.

Intracortical brain-computer interfaces (iBCIs) have allowed people with tetraplegia to control a computer cursor by imagining the movement of their paralyzed arm or hand. State-of-the-art decoders deployed in human iBCIs are derived from a Kalman filter that assumes Markov dynamics on the angle of intended movement, and a unimodal dependence on intended angle for each channel of neural activity. Due to errors made in the decoding of noisy neural data, as a user attempts to move the cursor to a goal, the angle between cursor and goal positions may change rapidly. We propose a dynamic Bayesian network that includes the on-screen goal position as part of its latent state, and thus allows the person’s intended angle of movement to be aggregated over a much longer history of neural activity. This multiscale model explicitly captures the relationship between instantaneous angles of motion and long-term goals, and incorporates semi-Markov dynamics for motion trajectories. We also introduce a multimodal likelihood model for recordings of neural populations which can be rapidly calibrated for clinical applications. In offline experiments with recorded neural data, we demonstrate significantly improved prediction of motion directions compared to the Kalman filter. We derive an efficient online inference algorithm, enabling a clinical trial participant with tetraplegia to control a computer cursor with neural activity in real time. The observed kinematics of cursor movement are objectively straighter and smoother than prior iBCI decoding models without loss of responsiveness.

Variants of max-product (MP) belief propagation effectively find modes of many complex graphical models, but are limited to discrete distributions. Diverse particle max-product (D-PMP) robustly approximates max-product updates in continuous MRFs using stochastically sampled particles, but previous work was specialized to tree-structured models. Motivated by the challenging problem of protein side chain prediction, we extend D-PMP in several key ways to create a generic MAP inference algorithm for loopy models. We define a modified diverse particle selection objective that is provably submodular, leading to an efficient greedy algorithm with rigorous optimality guarantees, and corresponding max-marginal error bounds. We further incorporate tree-reweighted variants of the MP algorithm to allow provable verification of global MAP recovery in many models. Our general-purpose Matlab library is applicable to a wide range of pairwise graphical models, and we validate our approach using optical flow benchmarks. We further demonstrate superior side chain prediction accuracy compared to baseline algorithms from the state-of-the-art Rosetta package.

In applications of graphical models arising in domains such as computer vision and signal processing, we often seek the most likely configurations of high-dimensional, continuous variables. We develop a particle-based max-product algorithm which maintains a diverse set of posterior mode hypotheses, and is robust to initialization. At each iteration, the set of hypotheses at each node is augmented via stochastic proposals, and then reduced via an efficient selection algorithm. The integer program underlying our optimization-based particle selection minimizes errors in subsequent max-product message updates. This objective automatically encourages diversity in the maintained hypotheses, without requiring tuning of application-specific distances among hypotheses. By avoiding the stochastic resampling steps underlying particle sum-product algorithms, we also avoid common degeneracies where particles collapse onto a single hypothesis. Our approach significantly outperforms previous particle-based algorithms in experiments focusing on the estimation of human pose from single images.

We develop convergent minimization algorithms for Bethe variational approximations which explicitly constrain marginal estimates to families of valid distributions. While existing message passing algorithms define fixed point iterations corresponding to stationary points of the Bethe free energy, their greedy dynamics do not distinguish between local minima and maxima, and can fail to converge. For continuous estimation problems, this instability is linked to the creation of invalid marginal estimates, such as Gaussians with negative variance. Conversely, our approach leverages multiplier methods with well-understood convergence properties, and uses bound projection methods to ensure that marginal approximations are valid at all iterations. We derive general algorithms for discrete and Gaussian pairwise Markov random fields, showing improvements over standard loopy belief propagation. We also apply our method to a hybrid model with both discrete and continuous variables, showing improvements over expectation propagation.