This paper considers the challenging tasks of Multi-Agent Reinforcement Learning (MARL) under partial observability, where each agent only sees her own individual observations and actions that reveal incomplete information about the underlying state of system. This paper studies these tasks under the general model of multiplayer general-sum Partially Observable Markov Games (POMGs), which is significantly larger than the standard model of Imperfect Information Extensive-Form Games (IIEFGs). We identify a rich subclass of POMGs -- weakly revealing POMGs -- in which sample-efficient learning is tractable. In the self-play setting, we prove that a simple algorithm combining optimism and Maximum Likelihood Estimation (MLE) is sufficient to find approximate Nash equilibria, correlated equilibria, as well as coarse correlated equilibria of weakly revealing POMGs, in a polynomial number of samples when the number of agents is small. In the setting of playing against adversarial opponents, we show that a variant of our optimistic MLE algorithm is capable of achieving sublinear regret when being compared against the optimal maximin policies. To our best knowledge, this work provides the first line of sample-efficient results for learning POMGs.

Dealing with non-stationarity in environments (e.g., in the transition dynamics) and objectives (e.g., in the reward functions) is a challenging problem that is crucial in real-world applications of reinforcement learning (RL). While most current approaches model the changes as a single shared embedding vector, we leverage insights from the recent causality literature to model non-stationarity in terms of individual latent change factors, and causal graphs across different environments. In particular, we propose Factored Adaptation for Non-Stationary RL (FANS-RL), a factored adaption approach that learns jointly both the causal structure in terms of a factored MDP, and a factored representation of the individual time-varying change factors. We prove that under standard assumptions, we can completely recover the causal graph representing the factored transition and reward function, as well as a partial structure between the individual change factors and the state components. Through our general framework, we can consider general non-stationary scenarios with different function types and changing frequency, including changes across episodes and within episodes. Experimental results demonstrate that FANS-RL outperforms existing approaches in terms of return, compactness of the latent state representation, and robustness to varying degrees of non-stationarity.

In Bayesian Networks (BNs), the direction of edges is crucial for causal reasoning and inference. However, Markov equivalence class considerations mean it is not always possible to establish edge orientations, which is why many BN structure learning algorithms cannot orientate all edges from purely observational data. Moreover, latent confounders can lead to false positive edges. Relatively few methods have been proposed to address these issues. In this work, we present the hybrid mFGS-BS (majority rule and Fast Greedy equivalence Search with Bayesian Scoring) algorithm for structure learning from discrete data that involves an observational data set and one or more interventional data sets. The algorithm assumes causal insufficiency in the presence of latent variables and produces a Partial Ancestral Graph (PAG). Structure learning relies on a hybrid approach and a novel Bayesian scoring paradigm that calculates the posterior probability of each directed edge being added to the learnt graph. Experimental results based on well-known networks of up to 109 variables and 10k sample size show that mFGS-BS improves structure learning accuracy relative to the state-of-the-art and it is computationally efficient.

Most previous work in music emotion recognition assumes a single or a few song-level labels for the whole song. While it is known that different emotions can vary in intensity within a song, annotated data for this setup is scarce and difficult to obtain. In this work, we propose a method to predict emotion dynamics in song lyrics without song-level supervision. We frame each song as a time series and employ a State Space Model (SSM), combining a sentence-level emotion predictor with an Expectation-Maximization (EM) procedure to generate the full emotion dynamics. Our experiments show that applying our method consistently improves the performance of sentence-level baselines without requiring any annotated songs, making it ideal for limited training data scenarios. Further analysis through case studies shows the benefits of our method while also indicating the limitations and pointing to future directions.

CVaR (Conditional Value at Risk) is a risk metric widely used in finance. However, dynamically optimizing CVaR is difficult since it is not a standard Markov decision process (MDP) and the principle of dynamic programming fails. In this paper, we study the infinite-horizon discrete-time MDP with a long-run CVaR criterion, from the view of sensitivity-based optimization. By introducing a pseudo CVaR metric, we derive a CVaR difference formula which quantifies the difference of long-run CVaR under any two policies. The optimality of deterministic policies is derived. We obtain a so-called Bellman local optimality equation for CVaR, which is a necessary and sufficient condition for local optimal policies and only necessary for global optimal policies. A CVaR derivative formula is also derived for providing more sensitivity information. Then we develop a policy iteration type algorithm to efficiently optimize CVaR, which is shown to converge to local optima in the mixed policy space. We further discuss some extensions including the mean-CVaR optimization and the maximization of CVaR. Finally, we conduct numerical experiments relating to portfolio management to demonstrate the main results. Our work may shed light on dynamically optimizing CVaR from a sensitivity viewpoint.

This paper aims to present the first Frequentist framework on signal region detection in high-resolution and high-order image regression problems. Image data and scalar-on-image regression are intensively studied in recent years. However, most existing studies on such topics focused on outcome prediction, while the research on image region detection is rather limited, even though the latter is often more important. In this paper, we develop a general framework named Sparse Kronecker Product Decomposition (SKPD) to tackle this issue. The SKPD framework is general in the sense that it works for both matrices (e.g., 2D grayscale images) and (high-order) tensors (e.g., 2D colored images, brain MRI/fMRI data) represented image data. Moreover, unlike many Bayesian approaches, our framework is computationally scalable for high-resolution image problems. Specifically, our framework includes: 1) the one-term SKPD; 2) the multi-term SKPD; and 3) the nonlinear SKPD. We propose nonconvex optimization problems to estimate the one-term and multi-term SKPDs and develop path-following algorithms for the nonconvex optimization. The computed solutions of the path-following algorithm are guaranteed to converge to the truth with a particularly chosen initialization even though the optimization is nonconvex. Moreover, the region detection consistency could also be guaranteed by the one-term and multi-term SKPD. The nonlinear SKPD is highly connected to shallow convolutional neural networks (CNN), particular to CNN with one convolutional layer and one fully connected layer. Effectiveness of SKPDs is validated by real brain imaging data in the UK Biobank database.

Deep learning (DL) applied to a device's radio-frequency fingerprint~(RFF) has attracted significant attention in physical-layer authentication due to its extraordinary classification performance. Conventional DL-RFF techniques are trained by adopting maximum likelihood estimation~(MLE). Although their discriminability has recently been extended to unknown devices in open-set scenarios, they still tend to overfit the channel statistics embedded in the training dataset. This restricts their practical applications as it is challenging to collect sufficient training data capturing the characteristics of all possible wireless channel environments. To address this challenge, we propose a DL framework of disentangled representation~(DR) learning that first learns to factor the signals into a device-relevant component and a device-irrelevant component via adversarial learning. Then, it shuffles these two parts within a dataset for implicit data augmentation, which imposes a strong regularization on RFF extractor learning to avoid the possible overfitting of device-irrelevant channel statistics, without collecting additional data from unknown channels. Experiments validate that the proposed approach, referred to as DR-based RFF, outperforms conventional methods in terms of generalizability to unknown devices even under unknown complicated propagation environments, e.g., dispersive multipath fading channels, even though all the training data are collected in a simple environment with dominated direct line-of-sight~(LoS) propagation paths.

Decision tree models such as CART (Breiman et al., 1984) and their ensembles such as Random Forests (Breiman, 2001) and Gradient Boosted Trees (Chen & Guestrin, 2016; Friedman, 2001) have proved to be enormously successful supervised learning algorithms, because they are able to combine non-parametric model fitting with implicit dimension reduction. It is often difficult to quantify the uncertainty of their predictions and due to their greedy local splitting criteria, there is no guarantee for the optimality of the constructed decision trees. An alternative approach is to construct the decision trees in a Bayesian manner (H. A. Chipman et al., 1998; Denison et al., 1998; Wu et al., 2007) To address these issues, H. A. Chipman et al., 1998 proposed a Bayesian adaptation of CART, Bayesian CART, and later, a sum of Bayesian CART trees, which they called Bayesian Additive Regression Trees (BART) (H. A. Chipman et al., 2010). One perspective views these algorithms as non-greedy stochastic versions of their deterministic equivalents, where the randomness inside the fitting process allows the algorithm to explore the space of possible decision trees in ways the CART algorithm cannot. An alternative perspective views these algorithms as Bayesian non-parametric regression models, in which we put a prior on the space of decision trees, assume a likelihood for the observed data, and then obtain a posterior distribution over the possible decision trees based on the training data. The posterior distribution can be used to provide posterior predictive credible intervals and other forms of uncertainty quantification.

Hidden semi-Markov Models (HSMM's) - while broadly in use - are restricted to a discrete and uniform time grid. They are thus not well suited to explain often irregularly spaced discrete event data from continuous-time phenomena. We show that non-sampling-based latent state inference used in HSMM's can be generalized to latent Continuous-Time semi-Markov Chains (CTSMC's). We formulate integro-differential forward and backward equations adjusted to the observation likelihood and introduce an exact integral equation for the Bayesian posterior marginals and a scalable Viterbi-type algorithm for posterior path estimates. The presented equations can be efficiently solved using well-known numerical methods. As a practical tool, variable-step HSMM's are introduced. We evaluate our approaches in latent state inference scenarios in comparison to classical HSMM's.

Abstract: UNet [27] is widely used in semantic segmentation due to its simplicity and effectiveness. However, its manually-designed architecture is applied to a large number of problem settings, either with no architecture optimizations, or with manual tuning, which is time consuming and can be sub-optimal. In this work, firstly, we propose Markov Random Field Neural Architecture Search (MRF-NAS) that extends and improves the recent Adaptive and Optimal Network Width Search (AOWS) method [4] with (i) a more general MRF framework (ii) diverse M-best loopy inference (iii) differentiable parameter learning. This provides the necessary NAS framework to efficiently explore network architectures that induce loopy inference graphs, including loops that arise from skip connections. With UNet as the backbone, we find an architecture, MRF-UNet, that shows several interesting characteristics.