While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-$k$ reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model called the Quantal Hierarchy model, which can relax both mutual consistency and best response while still approximating level-$k$, QRE, or typical Nash equilibrium behaviour in the limiting cases. The model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decision-making in extensive-form game tree. This representation enables us to treat simultaneous games in a similar manner to sequential games, where reasoning resources deplete throughout the game-tree. Bounds in player processing abilities are captured as information costs, where future branches of reasoning are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the effectiveness of the Quantal Hierarchy model in several canonical economic games, {both simultaneous and sequential}, using out-of-sample modelling.
Bayesian hierarchical mixture clustering (BHMC) improves traditionalBayesian hierarchical clustering by replacing conventional Gaussian-to-Gaussian kernels with a Hierarchical Dirichlet Process Mixture Model(HDPMM) for parent-to-child diffusion in the generative process. However,BHMC may produce trees with high nodal variance, indicating weak separation between nodes at higher levels. To address this issue, we employ Posterior Regularization, which imposes max-margin constraints on nodes at every level to enhance cluster separation. We illustrate how to apply PR toBHMC and demonstrate its effectiveness in improving the BHMC model.
We consider the problem of automatically synthesizing a hybrid controller for non-linear dynamical systems which ensures that the closed-loop fulfills an arbitrary \emph{Linear Temporal Logic} specification. Moreover, the specification may take into account logical context switches induced by an external environment or the system itself. Finally, we want to avoid classical brute-force time- and space-discretization for scalability. We achieve these goals by a novel two-layer strategy synthesis approach, where the controller generated in the lower layer provides invariant sets and basins of attraction, which are exploited at the upper logical layer in an abstract way. In order to achieve this, we provide new techniques for both the upper- and lower-level synthesis. Our new methodology allows to leverage both the computing power of state space control techniques and the intelligence of finite game solving for complex specifications, in a scalable way.
Reinforcement learning (RL) agents are known to be vulnerable to evasion attacks during deployment. In single-agent environments, attackers can inject imperceptible perturbations on the policy or value network's inputs or outputs; in multi-agent environments, attackers can control an adversarial opponent to indirectly influence the victim's observation. Adversarial policies offer a promising solution to craft such attacks. Still, current approaches either require perfect or partial knowledge of the victim policy or suffer from sample inefficiency due to the sparsity of task-related rewards. To overcome these limitations, we propose the Intrinsically Motivated Adversarial Policy (IMAP) for efficient black-box evasion attacks in single- and multi-agent environments without any knowledge of the victim policy. IMAP uses four intrinsic objectives based on state coverage, policy coverage, risk, and policy divergence to encourage exploration and discover stronger attacking skills. We also design a novel Bias-Reduction (BR) method to boost IMAP further. Our experiments demonstrate the effectiveness of these intrinsic objectives and BR in improving adversarial policy learning in the black-box setting against multiple types of victim agents in various single- and multi-agent MuJoCo environments. Notably, our IMAP reduces the performance of the state-of-the-art robust WocaR-PPO agents by 34\%-54\% and achieves a SOTA attacking success rate of 83.91\% in the two-player zero-sum game YouShallNotPass.
Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such changes in depth and breadth of knowledge as a partitioning of the problem space into regions of differing expertise. We provide here new algorithms that explicitly consider and adapt to the relationship between problem instances and experts' knowledge. We first propose and highlight the drawbacks of a naive approach based on nearest neighbor queries. To address these drawbacks we then introduce a novel algorithm - expertise trees - that constructs decision trees enabling the learner to select appropriate models. We provide theoretical insights and empirically validate the improved performance of our novel approach on a range of problems for which existing methods proved to be inadequate.
Model-based approaches to reinforcement learning (MBRL) exhibit favorable performance in practice, but their theoretical guarantees in large spaces are mostly restricted to the setting when transition model is Gaussian or Lipschitz, and demands a posterior estimate whose representational complexity grows unbounded with time. In this work, we develop a novel MBRL method (i) which relaxes the assumptions on the target transition model to belong to a generic family of mixture models; (ii) is applicable to large-scale training by incorporating a compression step such that the posterior estimate consists of a Bayesian coreset of only statistically significant past state-action pairs; and (iii) exhibits a sublinear Bayesian regret. To achieve these results, we adopt an approach based upon Stein's method, which, under a smoothness condition on the constructed posterior and target, allows distributional distance to be evaluated in closed form as the kernelized Stein discrepancy (KSD). The aforementioned compression step is then computed in terms of greedily retaining only those samples which are more than a certain KSD away from the previous model estimate. Experimentally, we observe that this approach is competitive with several state-of-the-art RL methodologies, and can achieve up-to 50 percent reduction in wall clock time in some continuous control environments.
Coronary CT angiography (CCTA) scans are widely used for diagnosis of coronary artery diseases. An accurate and automatic vessel labeling algorithm for CCTA analysis can significantly improve the diagnostic efficiency and reduce the clinicians'manual efforts. In this paper, we propose a simple vessel labeling method based on the Point Transformer, which only needs the coronary artery segmentation. Specifically, firstly, the coronary segmentation is transformed to point cloud. Then, these points are fed into the hierarchical transformer blocks to obtain the multi-level features, including local and global features. Finally, the network output the semantic classification points and map them to centerline labeling. This method is only based on the structure of coronary segmentation and need not other features, so it is easy to generalize to other vessel labeling tasks, e.g., head and neck vessel labeling. To evaluate the performance of our proposed method, CCTA scans of 53 subjects are collected in our experiment. The experimental results demonstrate the efficacy of this approach.
A number of information retrieval studies have been done to assess which statistical techniques are appropriate for comparing systems. However, these studies are focused on TREC-style experiments, which typically have fewer than 100 topics. There is no similar line of work for large search and recommendation experiments; such studies typically have thousands of topics or users and much sparser relevance judgements, so it is not clear if recommendations for analyzing traditional TREC experiments apply to these settings. In this paper, we empirically study the behavior of significance tests with large search and recommendation evaluation data. Our results show that the Wilcoxon and Sign tests show significantly higher Type-1 error rates for large sample sizes than the bootstrap, randomization and t-tests, which were more consistent with the expected error rate. While the statistical tests displayed differences in their power for smaller sample sizes, they showed no difference in their power for large sample sizes. We recommend the sign and Wilcoxon tests should not be used to analyze large scale evaluation results. Our result demonstrate that with Top-N recommendation and large search evaluation data, most tests would have a 100% chance of finding statistically significant results. Therefore, the effect size should be used to determine practical or scientific significance.
Multi-scale design has been considered in recent image super-resolution (SR) works to explore the hierarchical feature information. Existing multi-scale networks aim to build elaborate blocks or progressive architecture for restoration. In general, larger scale features concentrate more on structural and high-level information, while smaller scale features contain plentiful details and textured information. In this point of view, information from larger scale features can be derived from smaller ones. Based on the observation, in this paper, we build a sequential hierarchical learning super-resolution network (SHSR) for effective image SR. Specially, we consider the inter-scale correlations of features, and devise a sequential multi-scale block (SMB) to progressively explore the hierarchical information. SMB is designed in a recursive way based on the linearity of convolution with restricted parameters. Besides the sequential hierarchical learning, we also investigate the correlations among the feature maps and devise a distribution transformation block (DTB). Different from attention-based methods, DTB regards the transformation in a normalization manner, and jointly considers the spatial and channel-wise correlations with scaling and bias factors. Experiment results show SHSR achieves superior quantitative performance and visual quality to state-of-the-art methods with near 34\% parameters and 50\% MACs off when scaling factor is $\times4$. To boost the performance without further training, the extension model SHSR$^+$ with self-ensemble achieves competitive performance than larger networks with near 92\% parameters and 42\% MACs off with scaling factor $\times4$.
This article offers a new paradigm for analyzing the behavior of uncertain multivariable systems using a set of quantities we call \emph{inferential moments}. Marginalization is an uncertainty quantification process that averages conditional probabilities to quantify the \emph{expected value} of a probability of interest. Inferential moments are higher order conditional probability moments that describe how a distribution is expected to respond to new information. Of particular interest in this article is the \emph{inferential deviation}, which is the expected fluctuation of the probability of one variable in response to an inferential update of another. We find a power series expansion of the Mutual Information in terms of inferential moments, which implies that inferential moment logic may be useful for tasks typically performed with information theoretic tools. We explore this in two applications that analyze the inferential deviations of a Bayesian Network to improve situational awareness and decision-making. We implement a simple greedy algorithm for optimal sensor tasking using inferential deviations that generally outperforms a similar greedy Mutual Information algorithm in terms of predictive probabilistic error.
When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant.