Partially Observable Markov Decision Process (POMDP) is a framework applicable to many real world problems. In this work, we propose an approach to solve POMDPs with multimodal belief by relying on a policy that solves the fully observable version. By defininig a new, mixture value function based on the value function from the fully observable variant, we can use the corresponding greedy policy to solve the POMDP itself. We develop the mathematical framework necessary for discussion, and introduce a benchmark built on the task of Reconnaissance Blind TicTacToe. On this benchmark, we show that our policy outperforms policies ignoring the existence of multiple modes.
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The brain age has been proven to be a phenotype of relevance to cognitive performance and brain disease. Achieving accurate brain age prediction is an essential prerequisite for optimizing the predicted brain-age difference as a biomarker. As a comprehensive biological characteristic, the brain age is hard to be exploited accurately with models using feature engineering and local processing such as local convolution and recurrent operations that process one local neighborhood at a time. Instead, Vision Transformers learn global attentive interaction of patch tokens, introducing less inductive bias and modeling long-range dependencies. In terms of this, we proposed a novel network for learning brain age interpreting with global and local dependencies, where the corresponding representations are captured by Successive Permuted Transformer (SPT) and convolution blocks. The SPT brings computation efficiency and locates the 3D spatial information indirectly via continuously encoding 2D slices from different views. Finally, we collect a large cohort of 22645 subjects with ages ranging from 14 to 97 and our network performed the best among a series of deep learning methods, yielding a mean absolute error (MAE) of 2.855 in validation set, and 2.911 in an independent test set.
Exploration is critical for deep reinforcement learning in complex environments with high-dimensional observations and sparse rewards. To address this problem, recent approaches proposed to leverage intrinsic rewards to improve exploration, such as novelty-based exploration and prediction-based exploration. However, many intrinsic reward modules require sophisticated structures and representation learning, resulting in prohibitive computational complexity and unstable performance. In this paper, we propose Rewarding Episodic Visitation Discrepancy (REVD), a computation-efficient and quantified exploration method. More specifically, REVD provides intrinsic rewards by evaluating the R\'enyi divergence-based visitation discrepancy between episodes. To make efficient divergence estimation, a k-nearest neighbor estimator is utilized with a randomly-initialized state encoder. Finally, the REVD is tested on PyBullet Robotics Environments and Atari games. Extensive experiments demonstrate that REVD can significantly improves the sample efficiency of reinforcement learning algorithms and outperforms the benchmarking methods.
We consider the problem of learning the optimal threshold policy for control problems. Threshold policies make control decisions by evaluating whether an element of the system state exceeds a certain threshold, whose value is determined by other elements of the system state. By leveraging the monotone property of threshold policies, we prove that their policy gradients have a surprisingly simple expression. We use this simple expression to build an off-policy actor-critic algorithm for learning the optimal threshold policy. Simulation results show that our policy significantly outperforms other reinforcement learning algorithms due to its ability to exploit the monotone property. In addition, we show that the Whittle index, a powerful tool for restless multi-armed bandit problems, is equivalent to the optimal threshold policy for an alternative problem. This observation leads to a simple algorithm that finds the Whittle index by learning the optimal threshold policy in the alternative problem. Simulation results show that our algorithm learns the Whittle index much faster than several recent studies that learn the Whittle index through indirect means.
Training models on data obtained from randomized experiments is ideal for making good decisions. However, randomized experiments are often time-consuming, expensive, risky, infeasible or unethical to perform, leaving decision makers little choice but to rely on observational data collected under historical policies when training models. This opens questions regarding not only which decision-making policies would perform best in practice, but also regarding the impact of different data collection protocols on the performance of various policies trained on the data, or the robustness of policy performance with respect to changes in problem characteristics such as action- or reward- specific delays in observing outcomes. We aim to answer such questions for the problem of optimizing sales channel allocations at LinkedIn, where sales accounts (leads) need to be allocated to one of three channels, with the goal of maximizing the number of successful conversions over a period of time. A key problem feature constitutes the presence of stochastic delays in observing allocation outcomes, whose distribution is both channel- and outcome- dependent. We built a discrete-time simulation that can handle our problem features and used it to evaluate: a) a historical rule-based policy; b) a supervised machine learning policy (XGBoost); and c) multi-armed bandit (MAB) policies, under different scenarios involving: i) data collection used for training (observational vs randomized); ii) lead conversion scenarios; iii) delay distributions. Our simulation results indicate that LinUCB, a simple MAB policy, consistently outperforms the other policies, achieving a 18-47% lift relative to a rule-based policy
Lying on the heart of intelligent decision-making systems, how policy is represented and optimized is a fundamental problem. The root challenge in this problem is the large scale and the high complexity of policy space, which exacerbates the difficulty of policy learning especially in real-world scenarios. Towards a desirable surrogate policy space, recently policy representation in a low-dimensional latent space has shown its potential in improving both the evaluation and optimization of policy. The key question involved in these studies is by what criterion we should abstract the policy space for desired compression and generalization. However, both the theory on policy abstraction and the methodology on policy representation learning are less studied in the literature. In this work, we make very first efforts to fill up the vacancy. First, we propose a unified policy abstraction theory, containing three types of policy abstraction associated to policy features at different levels. Then, we generalize them to three policy metrics that quantify the distance (i.e., similarity) of policies, for more convenient use in learning policy representation. Further, we propose a policy representation learning approach based on deep metric learning. For the empirical study, we investigate the efficacy of the proposed policy metrics and representations, in characterizing policy difference and conveying policy generalization respectively. Our experiments are conducted in both policy optimization and evaluation problems, containing trust-region policy optimization (TRPO), diversity-guided evolution strategy (DGES) and off-policy evaluation (OPE). Somewhat naturally, the experimental results indicate that there is no a universally optimal abstraction for all downstream learning problems; while the influence-irrelevance policy abstraction can be a generally preferred choice.
Vision-based navigation requires processing complex information to make task-orientated decisions. Applications include autonomous robots, self-driving cars, and assistive vision for humans. One of the key elements in the process is the extraction and selection of relevant features in pixel space upon which to base action choices, for which Machine Learning techniques are well suited. However, Deep Reinforcement Learning agents trained in simulation often exhibit unsatisfactory results when deployed in the real-world due to perceptual differences known as the $\textit{reality gap}$. An approach that is yet to be explored to bridge this gap is self-attention. In this paper we (1) perform a systematic exploration of the hyperparameter space for self-attention based navigation of 3D environments and qualitatively appraise behaviour observed from different hyperparameter sets, including their ability to generalise; (2) present strategies to improve the agents' generalisation abilities and navigation behaviour; and (3) show how models trained in simulation are capable of processing real world images meaningfully in real time. To our knowledge, this is the first demonstration of a self-attention based agent successfully trained in navigating a 3D action space, using less than 4000 parameters.
We consider observations $(X,y)$ from single index models with unknown link function, Gaussian covariates and a regularized M-estimator $\hat\beta$ constructed from convex loss function and regularizer. In the regime where sample size $n$ and dimension $p$ are both increasing such that $p/n$ has a finite limit, the behavior of the empirical distribution of $\hat\beta$ and the predicted values $X\hat\beta$ has been previously characterized in a number of models: The empirical distributions are known to converge to proximal operators of the loss and penalty in a related Gaussian sequence model, which captures the interplay between ratio $p/n$, loss, regularization and the data generating process. This connection between$(\hat\beta,X\hat\beta)$ and the corresponding proximal operators require solving fixed-point equations that typically involve unobservable quantities such as the prior distribution on the index or the link function. This paper develops a different theory to describe the empirical distribution of $\hat\beta$ and $X\hat\beta$: Approximations of $(\hat\beta,X\hat\beta)$ in terms of proximal operators are provided that only involve observable adjustments. These proposed observable adjustments are data-driven, e.g., do not require prior knowledge of the index or the link function. These new adjustments yield confidence intervals for individual components of the index, as well as estimators of the correlation of $\hat\beta$ with the index. The interplay between loss, regularization and the model is thus captured in a data-driven manner, without solving the fixed-point equations studied in previous works. The results apply to both strongly convex regularizers and unregularized M-estimation. Simulations are provided for the square and logistic loss in single index models including logistic regression and 1-bit compressed sensing with 20\% corrupted bits.
In the well-known complexity class NP, many combinatorial problems can be found, whose optimization counterpart are important for many practical settings. Those problems usually consider full knowledge about the input and optimize on this specific input. In a practical setting, however, uncertainty in the input data is a usual phenomenon, whereby this is normally not covered in optimization versions of NP problems. One concept to model the uncertainty in the input data, is \textit{recoverable robustness}. In this setting, a solution on the input is calculated, whereby a possible recovery to a good solution should be guaranteed, whenever uncertainty manifests itself. That is, a solution $\texttt{s}_0$ for the base scenario $\textsf{S}_0$ as well as a solution \texttt{s} for every possible scenario of scenario set \textsf{S} has to be calculated. In other words, not only solution $\texttt{s}_0$ for instance $\textsf{S}_0$ is calculated but solutions \texttt{s} for all scenarios from \textsf{S} are prepared to correct possible errors through uncertainty. This paper introduces a specific concept of recoverable robust problems: Hamming Distance Recoverable Robust Problems. In this setting, solutions $\texttt{s}_0$ and \texttt{s} have to be calculated, such that $\texttt{s}_0$ and \texttt{s} may only differ in at most $\kappa$ elements. That is, one can recover from a harmful scenario by choosing a different solution, which is not too far away from the first solution. This paper surveys the complexity of Hamming distance recoverable robust version of optimization problems, typically found in NP for different types of scenarios. The complexity is primarily situated in the lower levels of the polynomial hierarchy. The main contribution of the paper is that recoverable robust problems with compression-encoded scenarios and $m \in \mathbb{N}$ recoveries are $\Sigma^P_{2m+1}$-complete.
The accurate and interpretable prediction of future events in time-series data often requires the capturing of representative patterns (or referred to as states) underpinning the observed data. To this end, most existing studies focus on the representation and recognition of states, but ignore the changing transitional relations among them. In this paper, we present evolutionary state graph, a dynamic graph structure designed to systematically represent the evolving relations (edges) among states (nodes) along time. We conduct analysis on the dynamic graphs constructed from the time-series data and show that changes on the graph structures (e.g., edges connecting certain state nodes) can inform the occurrences of events (i.e., time-series fluctuation). Inspired by this, we propose a novel graph neural network model, Evolutionary State Graph Network (EvoNet), to encode the evolutionary state graph for accurate and interpretable time-series event prediction. Specifically, Evolutionary State Graph Network models both the node-level (state-to-state) and graph-level (segment-to-segment) propagation, and captures the node-graph (state-to-segment) interactions over time. Experimental results based on five real-world datasets show that our approach not only achieves clear improvements compared with 11 baselines, but also provides more insights towards explaining the results of event predictions.
Sampling methods (e.g., node-wise, layer-wise, or subgraph) has become an indispensable strategy to speed up training large-scale Graph Neural Networks (GNNs). However, existing sampling methods are mostly based on the graph structural information and ignore the dynamicity of optimization, which leads to high variance in estimating the stochastic gradients. The high variance issue can be very pronounced in extremely large graphs, where it results in slow convergence and poor generalization. In this paper, we theoretically analyze the variance of sampling methods and show that, due to the composite structure of empirical risk, the variance of any sampling method can be decomposed into \textit{embedding approximation variance} in the forward stage and \textit{stochastic gradient variance} in the backward stage that necessities mitigating both types of variance to obtain faster convergence rate. We propose a decoupled variance reduction strategy that employs (approximate) gradient information to adaptively sample nodes with minimal variance, and explicitly reduces the variance introduced by embedding approximation. We show theoretically and empirically that the proposed method, even with smaller mini-batch sizes, enjoys a faster convergence rate and entails a better generalization compared to the existing methods.
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