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Most modern reinforcement learning algorithms optimize a cumulative single-step cost along a trajectory. The optimized motions are often 'unnatural', representing, for example, behaviors with sudden accelerations that waste energy and lack predictability. In this work, we present a novel paradigm of controlling nonlinear systems via the minimization of the Koopman spectrum cost: a cost over the Koopman operator of the controlled dynamics. This induces a broader class of dynamical behaviors that evolve over stable manifolds such as nonlinear oscillators, closed loops, and smooth movements. We demonstrate that some dynamics characterizations that are not possible with a cumulative cost are feasible in this paradigm, which generalizes the classical eigenstructure and pole assignments to nonlinear decision making. Moreover, we present a sample efficient online learning algorithm for our problem that enjoys a sub-linear regret bound under some structural assumptions.

This study modifies the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) algorithm for multi-modal optimization problems. The enhancements focus on addressing the challenges of multiple global minima, improving the algorithm's ability to maintain diversity and explore complex fitness landscapes. We incorporate niching strategies and dynamic adaptation mechanisms to refine the algorithm's performance in identifying and optimizing multiple global optima. The algorithm generates a population of candidate solutions by sampling from a multivariate normal distribution centered around the current mean vector, with the spread determined by the step size and covariance matrix. Each solution's fitness is evaluated as a weighted sum of its contributions to all global minima, maintaining population diversity and preventing premature convergence. We implemented the algorithm on 8 tunable composite functions for the GECCO 2024 Competition on Benchmarking Niching Methods for Multi-Modal Optimization (MMO), adhering to the competition's benchmarking framework. The results are presenting in many ways such as Peak Ratio, F1 score on various dimensions. They demonstrate the algorithm's robustness and effectiveness in handling both global optimization and MMO- specific challenges, providing a comprehensive solution for complex multi-modal optimization problems.

Score distillation sampling (SDS), the methodology in which the score from pretrained 2D diffusion models is distilled into 3D representation, has recently brought significant advancements in text-to-3D generation task. However, this approach is still confronted with critical geometric inconsistency problems such as the Janus problem. Starting from a hypothesis that such inconsistency problems may be induced by multiview inconsistencies between 2D scores predicted from various viewpoints, we introduce GSD, a simple and general plug-and-play framework for incorporating 3D consistency and therefore geometry awareness into the SDS process. Our methodology is composed of three components: 3D consistent noising, designed to produce 3D consistent noise maps that perfectly follow the standard Gaussian distribution, geometry-based gradient warping for identifying correspondences between predicted gradients of different viewpoints, and novel gradient consistency loss to optimize the scene geometry toward producing more consistent gradients. We demonstrate that our method significantly improves performance, successfully addressing the geometric inconsistency problems in text-to-3D generation task with minimal computation cost and being compatible with existing score distillation-based models. Our project page is available at //ku-cvlab.github.io/GSD/.

We study a nonconforming virtual element method (VEM) for advection-diffusion-reaction problems with continuous interior penalty (CIP) stabilization. The design of the method is based on a standard variational formulation of the problem (no skew-symmetrization), and boundary conditions are imposed with a Nitsche technique. We use the enhanced version of VEM, with a ``DoFi-DoFi'' stabilization in the diffusion and reaction terms. We prove stability of the proposed method and derive $h$-version error estimates.

Graphs have become a key tool when modeling and solving problems in different areas. The Floyd-Warshall (FW) algorithm computes the shortest path between all pairs of vertices in a graph and is employed in areas like communication networking, traffic routing, bioinformatics, among others. However, FW is computationally and spatially expensive since it requires O(n^3) operations and O(n^2) memory space. As the graph gets larger, parallel computing becomes necessary to provide a solution in an acceptable time range. In this paper, we studied a FW code developed for Xeon Phi KNL processors and adapted it to run on any Intel x86 processors, losing the specificity of the former. To do so, we verified one by one the optimizations proposed by the original code, making adjustments to the base code where necessary, and analyzing its performance on two Intel servers under different test scenarios. In addition, a new optimization was proposed to increase the concurrency degree of the parallel algorithm, which was implemented using two different synchronization mechanisms. The experimental results show that all optimizations were beneficial on the two x86 platforms selected. Last, the new optimization proposal improved performance by up to 23%.

Designing protein sequences with desired biological function is crucial in biology and chemistry. Recent machine learning methods use a surrogate sequence-function model to replace the expensive wet-lab validation. How can we efficiently generate diverse and novel protein sequences with high fitness? In this paper, we propose IsEM-Pro, an approach to generate protein sequences towards a given fitness criterion. At its core, IsEM-Pro is a latent generative model, augmented by combinatorial structure features from a separately learned Markov random fields (MRFs). We develop an Monte Carlo Expectation-Maximization method (MCEM) to learn the model. During inference, sampling from its latent space enhances diversity while its MRFs features guide the exploration in high fitness regions. Experiments on eight protein sequence design tasks show that our IsEM-Pro outperforms the previous best methods by at least 55% on average fitness score and generates more diverse and novel protein sequences.

In the realm of statistical learning, the increasing volume of accessible data and increasing model complexity necessitate robust methodologies. This paper explores two branches of robust Bayesian methods in response to this trend. The first is generalized Bayesian inference, which introduces a learning rate parameter to enhance robustness against model misspecifications. The second is Gibbs posterior inference, which formulates inferential problems using generic loss functions rather than probabilistic models. In such approaches, it is necessary to calibrate the spread of the posterior distribution by selecting a learning rate parameter. The study aims to enhance the generalized posterior calibration (GPC) algorithm proposed by [1]. Their algorithm chooses the learning rate to achieve the nominal frequentist coverage probability, but it is computationally intensive because it requires repeated posterior simulations for bootstrap samples. We propose a more efficient version of the GPC inspired by sequential Monte Carlo (SMC) samplers. A target distribution with a different learning rate is evaluated without posterior simulation as in the reweighting step in SMC sampling. Thus, the proposed algorithm can reach the desirable value within a few iterations. This improvement substantially reduces the computational cost of the GPC. Its efficacy is demonstrated through synthetic and real data applications.

Methods of causal discovery aim to identify causal structures in a data driven way. Existing algorithms are known to be unstable and sensitive to statistical errors, and are therefore rarely used with biomedical or epidemiological data. We present an algorithm that efficiently exploits temporal structure, so-called tiered background knowledge, for estimating causal structures. Tiered background knowledge is readily available from, e.g., cohort or registry data. When used efficiently it renders the algorithm more robust to statistical errors and ultimately increases accuracy in finite samples. We describe the algorithm and illustrate how it proceeds. Moreover, we offer formal proofs as well as examples of desirable properties of the algorithm, which we demonstrate empirically in an extensive simulation study. To illustrate its usefulness in practice, we apply the algorithm to data from a children's cohort study investigating the interplay of diet, physical activity and other lifestyle factors for health outcomes.

Cold-start problems are long-standing challenges for practical recommendations. Most existing recommendation algorithms rely on extensive observed data and are brittle to recommendation scenarios with few interactions. This paper addresses such problems using few-shot learning and meta learning. Our approach is based on the insight that having a good generalization from a few examples relies on both a generic model initialization and an effective strategy for adapting this model to newly arising tasks. To accomplish this, we combine the scenario-specific learning with a model-agnostic sequential meta-learning and unify them into an integrated end-to-end framework, namely Scenario-specific Sequential Meta learner (or s^2 meta). By doing so, our meta-learner produces a generic initial model through aggregating contextual information from a variety of prediction tasks while effectively adapting to specific tasks by leveraging learning-to-learn knowledge. Extensive experiments on various real-world datasets demonstrate that our proposed model can achieve significant gains over the state-of-the-arts for cold-start problems in online recommendation. Deployment is at the Guess You Like session, the front page of the Mobile Taobao.

Multi-relation Question Answering is a challenging task, due to the requirement of elaborated analysis on questions and reasoning over multiple fact triples in knowledge base. In this paper, we present a novel model called Interpretable Reasoning Network that employs an interpretable, hop-by-hop reasoning process for question answering. The model dynamically decides which part of an input question should be analyzed at each hop; predicts a relation that corresponds to the current parsed results; utilizes the predicted relation to update the question representation and the state of the reasoning process; and then drives the next-hop reasoning. Experiments show that our model yields state-of-the-art results on two datasets. More interestingly, the model can offer traceable and observable intermediate predictions for reasoning analysis and failure diagnosis, thereby allowing manual manipulation in predicting the final answer.