Optimizing a set of functions simultaneously by leveraging their similarity is called multi-task optimization. Current black-box multi-task algorithms only solve a finite set of tasks, even when the tasks originate from a continuous space. In this paper, we introduce Parametric-task MAP-Elites (PT-ME), a novel black-box algorithm to solve continuous multi-task optimization problems. This algorithm (1) solves a new task at each iteration, effectively covering the continuous space, and (2) exploits a new variation operator based on local linear regression. The resulting dataset of solutions makes it possible to create a function that maps any task parameter to its optimal solution. We show on two parametric-task toy problems and a more realistic and challenging robotic problem in simulation that PT-ME outperforms all baselines, including the deep reinforcement learning algorithm PPO.

Counterfactual reasoning is pivotal in human cognition and especially important for providing explanations and making decisions. While Judea Pearl's influential approach is theoretically elegant, its generation of a counterfactual scenario often requires interventions that are too detached from the real scenarios to be feasible. In response, we propose a framework of natural counterfactuals and a method for generating counterfactuals that are natural with respect to the actual world's data distribution. Our methodology refines counterfactual reasoning, allowing changes in causally preceding variables to minimize deviations from realistic scenarios. To generate natural counterfactuals, we introduce an innovative optimization framework that permits but controls the extent of backtracking with a naturalness criterion. Empirical experiments indicate the effectiveness of our method.

Multi-task learning (MTL) considers learning a joint model for multiple tasks by optimizing a convex combination of all task losses. To solve the optimization problem, existing methods use an adaptive weight updating scheme, where task weights are dynamically adjusted based on their respective losses to prioritize difficult tasks. However, these algorithms face a great challenge whenever label noise is present, in which case excessive weights tend to be assigned to noisy tasks that have relatively large Bayes optimal errors, thereby overshadowing other tasks and causing performance to drop across the board. To overcome this limitation, we propose Multi-Task Learning with Excess Risks (ExcessMTL), an excess risk-based task balancing method that updates the task weights by their distances to convergence instead. Intuitively, ExcessMTL assigns higher weights to worse-trained tasks that are further from convergence. To estimate the excess risks, we develop an efficient and accurate method with Taylor approximation. Theoretically, we show that our proposed algorithm achieves convergence guarantees and Pareto stationarity. Empirically, we evaluate our algorithm on various MTL benchmarks and demonstrate its superior performance over existing methods in the presence of label noise.

Analytics on large-scale graphs have posed significant challenges to computational efficiency and resource requirements. Recently, Graph condensation (GC) has emerged as a solution to address challenges arising from the escalating volume of graph data. The motivation of GC is to reduce the scale of large graphs to smaller ones while preserving essential information for downstream tasks. For a better understanding of GC and to distinguish it from other related topics, we present a formal definition of GC and establish a taxonomy that systematically categorizes existing methods into three types based on its objective, and classify the formulations to generate the condensed graphs into two categories as modifying the original graphs or synthetic completely new ones. Moreover, our survey includes a comprehensive analysis of datasets and evaluation metrics in this field. Finally, we conclude by addressing challenges and limitations, outlining future directions, and offering concise guidelines to inspire future research in this field.

Causal discovery, the task of inferring causal structure from data, promises to accelerate scientific research, inform policy making, and more. However, the per-dataset nature of existing causal discovery algorithms renders them slow, data hungry, and brittle. Inspired by foundation models, we propose a causal discovery framework where a deep learning model is pretrained to resolve predictions from classical discovery algorithms run over smaller subsets of variables. This method is enabled by the observations that the outputs from classical algorithms are fast to compute for small problems, informative of (marginal) data structure, and their structure outputs as objects remain comparable across datasets. Our method achieves state-of-the-art performance on synthetic and realistic datasets, generalizes to data generating mechanisms not seen during training, and offers inference speeds that are orders of magnitude faster than existing models.

Aligning language models (LMs) with curated human feedback is critical to control their behaviors in real-world applications. Several recent policy optimization methods, such as DPO and SLiC, serve as promising alternatives to the traditional Reinforcement Learning from Human Feedback (RLHF) approach. In practice, human feedback often comes in a format of a ranked list over multiple responses to amortize the cost of reading prompt. Multiple responses can also be ranked by reward models or AI feedback. There lacks such a study on directly fitting upon a list of responses. In this work, we formulate the LM alignment as a listwise ranking problem and describe the Listwise Preference Optimization (LiPO) framework, where the policy can potentially learn more effectively from a ranked list of plausible responses given the prompt. This view draws an explicit connection to Learning-to-Rank (LTR), where most existing preference optimization work can be mapped to existing ranking objectives, especially pairwise ones. Following this connection, we provide an examination of ranking objectives that are not well studied for LM alignment withDPO and SLiC as special cases when list size is two. In particular, we highlight a specific method, LiPO-{\lambda}, which leverages a state-of-the-art listwise ranking objective and weights each preference pair in a more advanced manner. We show that LiPO-{\lambda} can outperform DPO and SLiC by a clear margin on two preference alignment tasks.

Collaborative mapping of unknown environments can be done faster and more robustly than a single robot. However, a collaborative approach requires a distributed paradigm to be scalable and deal with communication issues. This work presents a fully distributed algorithm enabling a group of robots to collectively optimize the parameters of a Neural Radiance Field (NeRF). The algorithm involves the communication of each robot's trained NeRF parameters over a mesh network, where each robot trains its NeRF and has access to its own visual data only. Additionally, the relative poses of all robots are jointly optimized alongside the model parameters, enabling mapping with unknown relative camera poses. We show that multi-robot systems can benefit from differentiable and robust 3D reconstruction optimized from multiple NeRFs. Experiments on real-world and synthetic data demonstrate the efficiency of the proposed algorithm. See the website of the project for videos of the experiments and supplementary material(https://sites.google.com/view/di-nerf/home).

Our work aims to present a high-performance and modular sampling-based trajectory planning algorithm for autonomous vehicles. This algorithm is tailored to address the complex challenges in solution space construction and optimization problem formulation within the path planning domain. Our method employs a multi-objective optimization strategy for efficient navigation in static and highly dynamic environments, focusing on optimizing trajectory comfort, safety, and path precision. This algorithm was then used to analyze the algorithm performance and success rate in 1750 virtual complex urban and highway scenarios. Our results demonstrate fast calculation times (8ms for 800 trajectories), a high success rate in complex scenarios (88%), and easy adaptability with different modules presented. The most noticeable difference exhibited was the fast trajectory sampling, feasibility check, and cost evaluation step across various trajectory counts. While our study presents promising results, it's important to note that our assessments have been conducted exclusively in simulated environments, and real-world testing is required to fully validate our findings. The code and the additional modules used in this research are publicly available as open-source software and can be accessed at the following link: https://github.com/TUM-AVS/Frenetix-Motion-Planner.

Symbolic Machine Learning Prover (SMLP) is a tool and a library for system exploration based on data samples obtained by simulating or executing the system on a number of input vectors. SMLP aims at exploring the system based on this data by taking a grey-box approach: SMLP combines statistical methods of data exploration with building and exploring machine learning models in close feedback loop with the system's response, and exploring these models by combining probabilistic and formal methods. SMLP has been applied in industrial setting at Intel for analyzing and optimizing hardware designs at the analog level. SMLP is a general purpose tool and can be applied to systems that can be sampled and modeled by machine learning models.

In Hyperparameter Optimization (HPO), only the hyperparameter configuration with the best performance is chosen after performing several trials, then, discarding the effort of training all the models with every hyperparameter configuration trial and performing an ensemble of all them. This ensemble consists of simply averaging the model predictions or weighting the models by a certain probability. Recently, other more sophisticated ensemble strategies, such as the Caruana method or the stacking strategy has been proposed. On the one hand, the Caruana method performs well in HPO ensemble, since it is not affected by the effects of multicollinearity, which is prevalent in HPO. It just computes the average over a subset of predictions with replacement. But it does not benefit from the generalization power of a learning process. On the other hand, stacking methods include a learning procedure since a meta-learner is required to perform the ensemble. Yet, one hardly finds advice about which meta-learner is adequate. Besides, some meta-learners may suffer from the effects of multicollinearity or need to be tuned to reduce them. This paper explores meta-learners for stacking ensemble in HPO, free of hyperparameter tuning, able to reduce the effects of multicollinearity and considering the ensemble learning process generalization power. At this respect, the boosting strategy seems promising as a stacking meta-learner. In fact, it completely removes the effects of multicollinearity. This paper also proposes an implicit regularization in the classical boosting method and a novel non-parametric stop criterion suitable only for boosting and specifically designed for HPO. The synergy between these two improvements over boosting exhibits competitive and promising predictive power performance compared to other existing meta-learners and ensemble approaches for HPO other than the stacking ensemble.