This work introduces macro-action discovery using value-of-information (VoI) for robust and efficient planning in partially observable Markov decision processes (POMDPs). POMDPs are a powerful framework for planning under uncertainty. Previous approaches have used high-level macro-actions within POMDP policies to reduce planning complexity. However, macro-action design is often heuristic and rarely comes with performance guarantees. Here, we present a method for extracting belief-dependent, variable-length macro-actions directly from a low-level POMDP model. We construct macro-actions by chaining sequences of open-loop actions together when the task-specific value of information (VoI) --- the change in expected task performance caused by observations in the current planning iteration --- is low. Importantly, we provide performance guarantees on the resulting VoI macro-action policies in the form of bounded regret relative to the optimal policy. In simulated tracking experiments, we achieve higher reward than both closed-loop and hand-coded macro-action baselines, selectively using VoI macro-actions to reduce planning complexity while maintaining near-optimal task performance.

The coronavirus disease 2019 (COVID-19) global pandemic has led many countries to impose unprecedented lockdown measures in order to slow down the outbreak. Questions on whether governments have acted promptly enough, and whether lockdown measures can be lifted soon have since been central in public discourse. Data-driven models that predict COVID-19 fatalities under different lockdown policy scenarios are essential for addressing these questions, and for informing governments on future policy directions. To this end, this paper develops a Bayesian model for predicting the effects of COVID-19 containment policies in a global context -- we treat each country as a distinct data point, and exploit variations of policies across countries to learn country-specific policy effects. Our model utilizes a two-layer Gaussian process (GP) prior -- the lower layer uses a compartmental SEIR (Susceptible, Exposed, Infected, Recovered) model as a prior mean function with "country-and-policy-specific" parameters that capture fatality curves under different "counterfactual" policies within each country, whereas the upper layer is shared across all countries, and learns lower-layer SEIR parameters as a function of country features and policy indicators. Our model combines the solid mechanistic foundations of SEIR models (Bayesian priors) with the flexible data-driven modeling and gradient-based optimization routines of machine learning (Bayesian posteriors) -- i.e., the entire model is trained end-to-end via stochastic variational inference. We compare the projections of our model with other models listed by the Center for Disease Control (CDC), and provide scenario analyses for various lockdown and reopening strategies highlighting their impact on COVID-19 fatalities.

A core problem in cognitive science and machine learning is to understand how humans derive semantic representations from perceptual objects, such as color from an apple, pleasantness from a musical chord, or seriousness from a face. Markov Chain Monte Carlo with People (MCMCP) is a prominent method for studying such representations, in which participants are presented with binary choice trials constructed such that the decisions follow a Markov Chain Monte Carlo acceptance rule. However, while MCMCP has strong asymptotic properties, its binary choice paradigm generates relatively little information per trial, and its local proposal function makes it slow to explore the parameter space and find the modes of the distribution. Here we therefore generalize MCMCP to a continuous-sampling paradigm, where in each iteration the participant uses a slider to continuously manipulate a single stimulus dimension to optimize a given criterion such as'pleasantness'. We formulate both methods from a utility-theory perspective, and show that the new method can be interpreted as'Gibbs Sampling with People' (GSP). Further, we introduce an aggregation parameter to the transition step, and show that this parameter can be manipulated to flexibly shift between Gibbs sampling and deterministic optimization. In an initial study, we show GSP clearly outperforming MCMCP; we then show that GSP provides novel and interpretable results in three other domains, namely musical chords, vocal emotions, and faces.

Variational autoencoders (VAEs) are a popular framework for modeling complex data distributions; they can be efficiently trained via variational inference by maximizing the evidence lower bound (ELBO), at the expense of a gap to the exact (log-)marginal likelihood. While VAEs are commonly used for representation learning, it is unclear why ELBO maximization would yield useful representations, since unregularized maximum likelihood estimation cannot invert the data-generating process. Yet, VAEs often succeed at this task. We seek to elucidate this apparent paradox by studying nonlinear VAEs in the limit of near-deterministic decoders. We first prove that, in this regime, the optimal encoder approximately inverts the decoder---a commonly used but unproven conjecture---which we refer to as self-consistency. Leveraging self-consistency, we show that the ELBO converges to a regularized log-likelihood. This allows VAEs to perform what has recently been termed independent mechanism analysis (IMA): it adds an inductive bias towards decoders with column-orthogonal Jacobians, which helps recovering the true latent factors. The gap between ELBO and log-likelihood is therefore welcome, since it bears unanticipated benefits for nonlinear representation learning. In experiments on synthetic and image data, we show that VAEs uncover the true latent factors when the data generating process satisfies the IMA assumption.

We study regret minimization in non-episodic factored Markov decision processes (FMDPs), where all existing algorithms make the strong assumption that the factored structure of the FMDP is known to the learner in advance. In this paper, we provide the first algorithm that learns the structure of the FMDP while minimizing the regret. Our algorithm is based on the optimism in face of uncertainty principle, combined with a simple statistical method for structure learning, and can be implemented efficiently given oracle-access to an FMDP planner. Moreover, we give a variant of our algorithm that remains efficient even when the oracle is limited to non-factored actions, which is the case with almost all existing approximate planners. Finally, we leverage our techniques to prove a novel lower bound for the known structure case, closing the gap to the regret bound of Chen et al. [2021].

Latent variable models are ubiquitous in the exploratory analysis of neural population recordings, where they allow researchers to summarize the activity of large populations of neurons in lower dimensional'latent' spaces. Existing methods can generally be categorized into (i) Bayesian methods that facilitate flexible incorporation of prior knowledge and uncertainty estimation, but which typically do not scale to large datasets; and (ii) highly parameterized methods without explicit priors that scale better but often struggle in the low-data regime. Here, we bridge this gap by developing a fully Bayesian yet scalable version of Gaussian process factor analysis (bGPFA), which models neural data as arising from a set of inferred latent processes with a prior that encourages smoothness over time. Additionally, bGPFA uses automatic relevance determination to infer the dimensionality of neural activity directly from the training data during optimization. To enable the analysis of continuous recordings without trial structure, we introduce a novel variational inference strategy that scales near-linearly in time and also allows for non-Gaussian noise models appropriate for electrophysiological recordings.

Recently, model-based agents have achieved better performance than model-free ones using the same computational budget and training time in single-agent environments. However, due to the complexity of multi-agent systems, it is tough to learn the model of the environment. The significant compounding error may hinder the learning process when model-based methods are applied to multi-agent tasks. This paper proposes an implicit model-based multi-agent reinforcement learning method based on value decomposition methods. Under this method, agents can interact with the learned virtual environment and evaluate the current state value according to imagined future states in the latent space, making agents have the foresight. Our approach can be applied to any multi-agent value decomposition method. The experimental results show that our method improves the sample efficiency in different partially observable Markov decision process domains.

Reinforcement learning algorithms are widely used in domains where it is desirable to provide a personalized service. In these domains it is common that user data contains sensitive information that needs to be protected from third parties. Motivated by this, we study privacy in the context of finite-horizon Markov Decision Processes (MDPs) by requiring information to be obfuscated on the user side. We formulate this notion of privacy for RL by leveraging the local differential privacy (LDP) framework. We establish a lower bound for regret minimization in finite-horizon MDPs with LDP guarantees which shows that guaranteeing privacy has a multiplicative effect on the regret. This result shows that while LDP is an appealing notion of privacy, it makes the learning problem significantly more complex. Finally, we present an optimistic algorithm that simultaneously satisfies $\varepsilon$-LDP requirements, and achieves $\sqrt{K}/\varepsilon$ regret in any finite-horizon MDP after $K$ episodes, matching the lower bound dependency on the number of episodes $K$.

Although the foundations of ranking are well established, the ranking literature has primarily been focused on simple, unimodal models, e.g. the Mallows and Plackett-Luce models, that define distributions centered around a single total ordering. Explicit mixture models have provided some tools for modelling multimodal ranking data, though learning such models from data is often difficult. In this work, we contribute a contextual repeated selection (CRS) model that leverages recent advances in choice modeling to bring a natural multimodality and richness to the rankings space. We provide rigorous theoretical guarantees for maximum likelihood estimation under the model through structure-dependent tail risk and expected risk bounds. As a by-product, we also furnish the first tight bounds on the expected risk of maximum likelihood estimators for the multinomial logit (MNL) choice model and the Plackett-Luce (PL) ranking model, as well as the first tail risk bound on the PL ranking model. The CRS model significantly outperforms existing methods for modeling real world ranking data in a variety of settings, from racing to rank choice voting.

Gaussian latent variable models are a key class of Bayesian hierarchical models with applications in many fields. Performing Bayesian inference on such models can be challenging as Markov chain Monte Carlo algorithms struggle with the geometry of the resulting posterior distribution and can be prohibitively slow. An alternative is to use a Laplace approximation to marginalize out the latent Gaussian variables and then integrate out the remaining hyperparameters using dynamic Hamiltonian Monte Carlo, a gradient-based Markov chain Monte Carlo sampler. To implement this scheme efficiently, we derive a novel adjoint method that propagates the minimal information needed to construct the gradient of the approximate marginal likelihood. This strategy yields a scalable differentiation method that is orders of magnitude faster than state of the art differentiation techniques when the hyperparameters are high dimensional. We prototype the method in the probabilistic programming framework Stan and test the utility of the embedded Laplace approximation on several models, including one where the dimension of the hyperparameter is 6,000. Depending on the cases, the benefits can include an alleviation of the geometric pathologies that frustrate Hamiltonian Monte Carlo and a dramatic speed-up.