While the Bayesian decision-theoretic framework offers an elegant solution to the problem of decision making under uncertainty, one question is how to appropriately select the prior distribution. One idea is to employ a worst-case prior. However, this is not as easy to specify in sequential decision making as in simple statistical estimation problems. This paper studies (sometimes approximate) minimax-Bayes solutions for various reinforcement learning problems to gain insights into the properties of the corresponding priors and policies. We find that while the worst-case prior depends on the setting, the corresponding minimax policies are more robust than those that assume a standard (i.e. uniform) prior.

We study repeated bilateral trade where an adaptive $\sigma$-smooth adversary generates the valuations of sellers and buyers. We provide a complete characterization of the regret regimes for fixed-price mechanisms under different feedback models in the two cases where the learner can post either the same or different prices to buyers and sellers. We begin by showing that the minimax regret after $T$ rounds is of order $\sqrt{T}$ in the full-feedback scenario. Under partial feedback, any algorithm that has to post the same price to buyers and sellers suffers worst-case linear regret. However, when the learner can post two different prices at each round, we design an algorithm enjoying regret of order $T^{3/4}$ ignoring log factors. We prove that this rate is optimal by presenting a surprising $T^{3/4}$ lower bound, which is the main technical contribution of the paper.

Many games are reliant on creating new and engaging content constantly to maintain the interest of their player-base. One such example are puzzle games, in such it is common to have a recurrent need to create new puzzles. Creating new puzzles requires guaranteeing that they are solvable and interesting to players, both of which require significant time from the designers. Automatic validation of puzzles provides designers with a significant time saving and potential boost in quality. Automation allows puzzle designers to estimate different properties, increase the variety of constraints, and even personalize puzzles to specific players. Puzzles often have a large design space, which renders exhaustive search approaches infeasible, if they require significant time. Specifically, those puzzles can be formulated as quadratic combinatorial optimization problems. This paper presents an evolutionary algorithm, empowered by expert-knowledge informed heuristics, for solving logical puzzles in video games efficiently, leading to a more efficient design process. We discuss multiple variations of hybrid genetic approaches for constraint satisfaction problems that allow us to find a diverse set of near-optimal solutions for puzzles. We demonstrate our approach on a fantasy Party Building Puzzle game, and discuss how it can be applied more broadly to other puzzles to guide designers in their creative process.

Ego-localization is a crucial task for autonomous vehicles. On the one hand, it needs to be very accurate, and on the other hand, very robust to provide reliable pose (position and orientation) information, even in challenging environments. Finding the best ego-position is usually tied to optimizing an objective function based on the sensor measurements. The most common approach is to maximize the likelihood, which leads under the assumption of normally distributed random variables to the well-known least squares minimization, often used in conjunction with recursive estimation, e. g. using a Kalman filter. However, least squares minimization is inherently sensitive to outliers, and consequently, more robust loss functions, such as L1 norm or Huber loss have been proposed. Arguably the most robust loss function is the outlier count, also known as maximum consensus optimization, where the outcome is independent of the outlier magnitude. In this paper, we investigate in detail the performance of maximum consensus localization based on LiDAR data. We elaborate on its shortcomings and propose a novel objective function based on Helmert's point error. In an experiment using 3001 measurement epochs, we show that the maximum consensus localization based on the introduced objective function provides superior results with respect to robustness.

The approximate nearest neighbor (ANN) search problem is fundamental to efficiently serving many real-world machine learning applications. A number of techniques have been developed for ANN search that are efficient, accurate, and scalable. However, such techniques typically have a number of parameters that affect the speed-recall tradeoff, and exhibit poor performance when such parameters aren't properly set. Tuning these parameters has traditionally been a manual process, demanding in-depth knowledge of the underlying search algorithm. This is becoming an increasingly unrealistic demand as ANN search grows in popularity. To tackle this obstacle to ANN adoption, this work proposes a constrained optimization-based approach to tuning quantization-based ANN algorithms. Our technique takes just a desired search cost or recall as input, and then generates tunings that, empirically, are very close to the speed-recall Pareto frontier and give leading performance on standard benchmarks.

This paper introduces a new extragradient-type algorithm for a class of nonconvex-nonconcave minimax problems. It is well-known that finding a local solution for general minimax problems is computationally intractable. This observation has recently motivated the study of structures sufficient for convergence of first order methods in the more general setting of variational inequalities when the so-called weak Minty variational inequality (MVI) holds. This problem class captures non-trivial structures as we demonstrate with examples, for which a large family of existing algorithms provably converge to limit cycles. Our results require a less restrictive parameter range in the weak MVI compared to what is previously known, thus extending the applicability of our scheme. The proposed algorithm is applicable to constrained and regularized problems, and involves an adaptive stepsize allowing for potentially larger stepsizes. Our scheme also converges globally even in settings where the underlying operator exhibits limit cycles.

Stochastic gradient descent-ascent (SGDA) is one of the main workhorses for solving finite-sum minimax optimization problems. Most practical implementations of SGDA randomly reshuffle components and sequentially use them (i.e., without-replacement sampling); however, there are few theoretical results on this approach for minimax algorithms, especially outside the easier-to-analyze (strongly-)monotone setups. To narrow this gap, we study the convergence bounds of SGDA with random reshuffling (SGDA-RR) for smooth nonconvex-nonconcave objectives with Polyak-{\L}ojasiewicz (P{\L}) geometry. We analyze both simultaneous and alternating SGDA-RR for nonconvex-P{\L} and primal-P{\L}-P{\L} objectives, and obtain convergence rates faster than with-replacement SGDA. Our rates extend to mini-batch SGDA-RR, recovering known rates for full-batch gradient descent-ascent (GDA). Lastly, we present a comprehensive lower bound for GDA with an arbitrary step-size ratio, which matches the full-batch upper bound for the primal-P{\L}-P{\L} case.

Autonomous exploration is a widely studied fundamental application in the field of quadrotors, which requires them to automatically explore unknown space to obtain complete information about the environment. The frontier-based method, which is one of the representative works on autonomous exploration, drives autonomous determination by the definition of frontier information, so that complete information about the environment is available to the quadrotor. However, existing frontier-based methods are able to accomplish the task but still suffer from inefficient exploration. How to improve the efficiency of autonomous exploration is the focus of current research. Typical problems include slow frontier generation, which affects real-time viewpoint determination, and insufficient determination methods that affect the quality of viewpoints. Therefore, to overcome these problems, this paper proposes a two-level viewpoint determination method for frontier-based autonomous exploration. Firstly, a sampling-based frontier detection method is presented for faster frontier generation, which improves the immediacy of environmental representation compared to traditional traversal-based methods. Secondly, we consider the access to environmental information during flight for the first time and design an innovative heuristic evaluation function to decide on a high-quality viewpoint as the next local navigation target in each exploration iteration. We conducted extensive benchmark and real-world tests to validate our method. The results confirm that our method optimizes the frontier search time by 85%, the exploration time by around 20-30%, and the exploration path by 25-35%.

This paper presents a quantum-based Fourier-regression approach for machine learning hyperparameter optimization applied to a benchmark of models trained on a dataset related to a forecast problem in the airline industry. Our approach utilizes the Fourier series method to represent the hyperparameter search space, which is then optimized using quantum algorithms to find the optimal set of hyperparameters for a given machine learning model. Our study evaluates the proposed method on a benchmark of models trained to predict a forecast problem in the airline industry using a standard HyperParameter Optimizer (HPO). The results show that our approach outperforms traditional hyperparameter optimization methods in terms of accuracy and convergence speed for the given search space. Our study provides a new direction for future research in quantum-based machine learning hyperparameter optimization.

Many real-world data can be modeled as heterogeneous graphs that contain multiple types of nodes and edges. Meanwhile, due to excellent performance, heterogeneous graph neural networks (GNNs) have received more and more attention. However, the existing work mainly focuses on the design of novel GNN models, while ignoring another important issue that also has a large impact on the model performance, namely the missing attributes of some node types. The handcrafted attribute completion requires huge expert experience and domain knowledge. Also, considering the differences in semantic characteristics between nodes, the attribute completion should be fine-grained, i.e., the attribute completion operation should be node-specific. Moreover, to improve the performance of the downstream graph learning task, attribute completion and the training of the heterogeneous GNN should be jointly optimized rather than viewed as two separate processes. To address the above challenges, we propose a differentiable attribute completion framework called AutoAC for automated completion operation search in heterogeneous GNNs. We first propose an expressive completion operation search space, including topology-dependent and topology-independent completion operations. Then, we propose a continuous relaxation schema and further propose a differentiable completion algorithm where the completion operation search is formulated as a bi-level joint optimization problem. To improve the search efficiency, we leverage two optimization techniques: discrete constraints and auxiliary unsupervised graph node clustering. Extensive experimental results on real-world datasets reveal that AutoAC outperforms the SOTA handcrafted heterogeneous GNNs and the existing attribute completion method