A conceptually appealing approach for learning Extensive-Form Games (EFGs) is to convert them to Normal-Form Games (NFGs). This approach enables us to directly translate state-of-the-art techniques and analyses in NFGs to learning EFGs, but typically suffers from computational intractability due to the exponential blow-up of the game size introduced by the conversion. In this paper, we address this problem in natural and important setups for the \emph{$\Phi$-Hedge} algorithm -- A generic algorithm capable of learning a large class of equilibria for NFGs. We show that $\Phi$-Hedge can be directly used to learn Nash Equilibria (zero-sum settings), Normal-Form Coarse Correlated Equilibria (NFCCE), and Extensive-Form Correlated Equilibria (EFCE) in EFGs. We prove that, in those settings, the \emph{$\Phi$-Hedge} algorithms are equivalent to standard Online Mirror Descent (OMD) algorithms for EFGs with suitable dilated regularizers, and run in polynomial time. This new connection further allows us to design and analyze a new class of OMD algorithms based on modifying its log-partition function. In particular, we design an improved algorithm with balancing techniques that achieves a sharp $\widetilde{\mathcal{O}}(\sqrt{XAT})$ EFCE-regret under bandit-feedback in an EFG with $X$ information sets, $A$ actions, and $T$ episodes. To our best knowledge, this is the first such rate and matches the information-theoretic lower bound.
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In this work, we consider the numerical computation of ground states and dynamics of single-component Bose-Einstein condensates (BECs). The corresponding models are spatially discretized with a multiscale finite element approach known as Localized Orthogonal Decomposition (LOD). Despite the outstanding approximation properties of such a discretization in the context of BECs, taking full advantage of it without creating severe computational bottlenecks can be tricky. In this paper, we therefore present two fully-discrete numerical approaches that are formulated in such a way that they take special account of the structure of the LOD spaces. One approach is devoted to the computation of ground states and another one for the computation of dynamics. A central focus of this paper is also the discussion of implementation aspects that are very important for the practical realization of the methods. In particular, we discuss the use of suitable data structures that keep the memory costs economical. The paper concludes with various numerical experiments in 1d, 2d and 3d that investigate convergence rates and approximation properties of the methods and which demonstrate their performance and computational efficiency, also in comparison to spectral and standard finite element approaches.
Rate-Splitting Multiple Access (RSMA) has recently found favour in the multi-antenna-aided wireless downlink, as a benefit of relaxing the accuracy of Channel State Information at the Transmitter (CSIT), while in achieving high spectral efficiency and providing security guarantees. These benefits are particularly important in high-velocity vehicular platoons since their high Doppler affects the estimation accuracy of the CSIT. To tackle this challenge, we propose an RSMA-based Internet of Vehicles (IoV) solution that jointly considers platoon control and FEderated Edge Learning (FEEL) in the downlink. Specifically, the proposed framework is designed for transmitting the unicast control messages within the IoV platoon, as well as for privacy-preserving FEEL-aided downlink Non-Orthogonal Unicasting and Multicasting (NOUM). Given this sophisticated framework, a multi-objective optimization problem is formulated to minimize both the latency of the FEEL downlink and the deviation of the vehicles within the platoon. To efficiently solve this problem, a Block Coordinate Descent (BCD) framework is developed for decoupling the main multi-objective problem into two sub-problems. Then, for solving these non-convex sub-problems, a Successive Convex Approximation (SCA) and Model Predictive Control (MPC) method is developed for solving the FEEL-based downlink problem and platoon control problem, respectively. Our simulation results show that the proposed RSMA-based IoV system outperforms the conventional systems.
Autoregressive processes naturally arise in a large variety of real-world scenarios, including e.g., stock markets, sell forecasting, weather prediction, advertising, and pricing. When addressing a sequential decision-making problem in such a context, the temporal dependence between consecutive observations should be properly accounted for converge to the optimal decision policy. In this work, we propose a novel online learning setting, named Autoregressive Bandits (ARBs), in which the observed reward follows an autoregressive process of order $k$, whose parameters depend on the action the agent chooses, within a finite set of $n$ actions. Then, we devise an optimistic regret minimization algorithm AutoRegressive Upper Confidence Bounds (AR-UCB) that suffers regret of order $\widetilde{\mathcal{O}} \left( \frac{(k+1)^{3/2}\sqrt{nT}}{(1-\Gamma)^2} \right)$, being $T$ the optimization horizon and $\Gamma < 1$ an index of the stability of the system. Finally, we present a numerical validation in several synthetic and one real-world setting, in comparison with general and specific purpose bandit baselines showing the advantages of the proposed approach.
We study time-inhomogeneous episodic reinforcement learning (RL) under general function approximation and sparse rewards. We design a new algorithm, Variance-weighted Optimistic $Q$-Learning (VO$Q$L), based on $Q$-learning and bound its regret assuming completeness and bounded Eluder dimension for the regression function class. As a special case, VO$Q$L achieves $\tilde{O}(d\sqrt{HT}+d^6H^{5})$ regret over $T$ episodes for a horizon $H$ MDP under ($d$-dimensional) linear function approximation, which is asymptotically optimal. Our algorithm incorporates weighted regression-based upper and lower bounds on the optimal value function to obtain this improved regret. The algorithm is computationally efficient given a regression oracle over the function class, making this the first computationally tractable and statistically optimal approach for linear MDPs.
Despite the significant interest and progress in reinforcement learning (RL) problems with adversarial corruption, current works are either confined to the linear setting or lead to an undesired $\tilde{O}(\sqrt{T}\zeta)$ regret bound, where $T$ is the number of rounds and $\zeta$ is the total amount of corruption. In this paper, we consider the contextual bandit with general function approximation and propose a computationally efficient algorithm to achieve a regret of $\tilde{O}(\sqrt{T}+\zeta)$. The proposed algorithm relies on the recently developed uncertainty-weighted least-squares regression from linear contextual bandit \citep{he2022nearly} and a new weighted estimator of uncertainty for the general function class. In contrast to the existing analysis that heavily relies on the linear structure, we develop a novel technique to control the sum of weighted uncertainty, thus establishing the final regret bounds. We then generalize our algorithm to the episodic MDP setting and first achieve an additive dependence on the corruption level $\zeta$ in the scenario of general function approximation. Notably, our algorithms achieve regret bounds either nearly match the performance lower bound or improve the existing methods for all the corruption levels and in both known and unknown $\zeta$ cases.
We study a type of generalized recursive game introduced by Castronova, Chen, and Zumbrun featuring increasing stakes, with an emphasis on continuous guts poker and $1$ v. $n$ coalitions. Our main results are to develop practical numerical algorithms with rigorous underlying theory for the approximation of optimal mutiplayer strategies, and to use these to obtain a number of interesting observations about guts. Outcomes are a striking 2-strategy optimum for $n$-player coalitions, with asymptotic advantage approximately $16\%$; convergence of Fictitious Play to symmetric Nash equilibrium; and a malevolent interactive $n$-player "bot" for demonstration.
Machine Learning as a service (MLaaS) permits resource-limited clients to access powerful data analytics services ubiquitously. Despite its merits, MLaaS poses significant concerns regarding the integrity of delegated computation and the privacy of the server's model parameters. To address this issue, Zhang et al. (CCS'20) initiated the study of zero-knowledge Machine Learning (zkML). Few zkML schemes have been proposed afterward; however, they focus on sole ML classification algorithms that may not offer satisfactory accuracy or require large-scale training data and model parameters, which may not be desirable for some applications. We propose ezDPS, a new efficient and zero-knowledge ML inference scheme. Unlike prior works, ezDPS is a zkML pipeline in which the data is processed in multiple stages for high accuracy. Each stage of ezDPS is harnessed with an established ML algorithm that is shown to be effective in various applications, including Discrete Wavelet Transformation, Principal Components Analysis, and Support Vector Machine. We design new gadgets to prove ML operations effectively. We fully implemented ezDPS and assessed its performance on real datasets. Experimental results showed that ezDPS achieves one-to-three orders of magnitude more efficient than the generic circuit-based approach in all metrics while maintaining more desirable accuracy than single ML classification approaches.
The computation of a solution concept of a cooperative game usually depends on values of all coalitions. However, in some applications, values of some of the coalitions might be unknown due to various reasons. We introduce a method to approximate standard solution concepts based only on partial information given by a so called incomplete game. We demonstrate the ideas on the class of minimal incomplete games. Approximations are derived for different solution concepts including the Shapley value, the nucleolus, or the core. We show explicit formulas for approximations of some of the solution concepts and show how the approximability differs based on additional information about the game.
User engagement is a critical metric for evaluating the quality of open-domain dialogue systems. Prior work has focused on conversation-level engagement by using heuristically constructed features such as the number of turns and the total time of the conversation. In this paper, we investigate the possibility and efficacy of estimating utterance-level engagement and define a novel metric, {\em predictive engagement}, for automatic evaluation of open-domain dialogue systems. Our experiments demonstrate that (1) human annotators have high agreement on assessing utterance-level engagement scores; (2) conversation-level engagement scores can be predicted from properly aggregated utterance-level engagement scores. Furthermore, we show that the utterance-level engagement scores can be learned from data. These scores can improve automatic evaluation metrics for open-domain dialogue systems, as shown by correlation with human judgements. This suggests that predictive engagement can be used as a real-time feedback for training better dialogue models.
Retrieving object instances among cluttered scenes efficiently requires compact yet comprehensive regional image representations. Intuitively, object semantics can help build the index that focuses on the most relevant regions. However, due to the lack of bounding-box datasets for objects of interest among retrieval benchmarks, most recent work on regional representations has focused on either uniform or class-agnostic region selection. In this paper, we first fill the void by providing a new dataset of landmark bounding boxes, based on the Google Landmarks dataset, that includes $94k$ images with manually curated boxes from $15k$ unique landmarks. Then, we demonstrate how a trained landmark detector, using our new dataset, can be leveraged to index image regions and improve retrieval accuracy while being much more efficient than existing regional methods. In addition, we further introduce a novel regional aggregated selective match kernel (R-ASMK) to effectively combine information from detected regions into an improved holistic image representation. R-ASMK boosts image retrieval accuracy substantially at no additional memory cost, while even outperforming systems that index image regions independently. Our complete image retrieval system improves upon the previous state-of-the-art by significant margins on the Revisited Oxford and Paris datasets. Code and data will be released.
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