Continual fine-tuning of Large Language Models (LLMs) is hampered by the trade-off between efficiency and expressiveness. Low-Rank Adaptation (LoRA) offers efficiency but constrains the model's ability to learn new tasks and transfer knowledge due to its low-rank nature and reliance on explicit parameter constraints. We propose GORP (Gradient LOw Rank Projection) for Continual Learning, a novel training strategy that overcomes these limitations by synergistically combining full and low-rank parameters and jointly updating within a unified low-rank gradient subspace. GORP expands the optimization space while preserving efficiency and mitigating catastrophic forgetting. Extensive experiments on continual learning benchmarks demonstrate GORP's superior performance compared to existing state-of-the-art approaches. Code is available at https://github.com/Wcxwcxw/GORP.

Post-training processes are essential phases in grounding pre-trained language models to real-world tasks, with learning from demonstrations or preference signals playing a crucial role in this adaptation. We present a unified theoretical framework bridging Supervised Fine-Tuning (SFT) and preference learning in Large Language Model (LLM) post-training. Through rigorous mathematical derivation, we demonstrate that both SFT and preference learning methods like Direct Preference Optimization (DPO) operate within the same optimal policy-reward subspace, with SFT representing a special case of implicit reward learning. Our analysis reveals a critical limitation in conventional SFT: the KL divergence term in distribution matching becomes constant with respect to the policy during optimization, failing to constrain model updates. To address this, we propose a simple yet effective learning rate reduction approach that yields significant performance improvements (up to \textbf{25\%} relative gain and \textbf{6\%} absolute win rate increase in instruction following tasks. Additionally, we derive alternative SFT objectives from various f-divergence functions that preserve the KL term during optimization, further enhancing post-DPO model performance. Finally, we extend the theoretical relationship between LLM logits and Q-functions from preference learning to the SFT context, providing mathematical derivations and experimental validation.

-- T eleoperation with non-haptic VR controllers deprives human operators of critical motion feedback. We address this by embedding a multi-objective optimization problem that converts user input into collision-free UR5e joint trajectories while actively suppressing liquid slosh in a glass. The controller maintains 13 ms average planning latency, confirming real-time performance and motivating the augmentation of this teleoperation approach to further objectives. Teleoperation enables humans to interact with the environment in remote places. Especially inaccessible hazardous environments have been named in research.

Major advertising platforms recently increased privacy protections by limiting advertisers' access to individual-level data. Instead of providing access to granular raw data, the platforms only allow a limited number of aggregate queries to a dataset, which is further protected by adding differentially private noise. This paper studies whether and how advertisers can design effective targeting policies within these restrictive privacy preserving data environments. To achieve this, I develop a probabilistic machine learning method based on Bayesian optimization, which facilitates dynamic data exploration. Since Bayesian optimization was designed to sample points from a function to find its maximum, it is not applicable to aggregate queries and to targeting. Therefore, I introduce two innovations: (i) integral updating of posteriors which allows to select the best regions of the data to query rather than individual points and (ii) a targeting-aware acquisition function that dynamically selects the most informative regions for the targeting task. I identify the conditions of the dataset and privacy environment that necessitate the use of such a "smart" querying strategy. I apply the strategic querying method to the Criteo AI Labs dataset for uplift modeling (Diemert et al., 2018) that contains visit and conversion data from 14M users. I show that an intuitive benchmark strategy only achieves 33% of the non-privacy-preserving targeting potential in some cases, while my strategic querying method achieves 97-101% of that potential, and is statistically indistinguishable from Causal Forest (Athey et al., 2019): a state-of-the-art non-privacy-preserving machine learning targeting method.

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

Recent years have seen rapid increases in intermittent renewable generation, requiring novel battery energy storage systems (BESS) solutions. One recent trend is the emergence of large grid-connected batteries, that can be controlled to provide multiple storage and flexibility services, using a stacked revenue model. Another emerging development is renewable energy communities (REC), in which prosumers invest in their own renewable generation capacity, but also requiring battery storage for flexibility. In this paper, we study settings in which energy communities rent battery capacity from a battery operator through a battery-as-a-service (BaaS) model. We present a methodology for determining the sizing and pricing of battery capacity that can be rented, such that it provides economic benefits to both the community and the battery operator that participates in the energy market. We examine how sizes and prices vary across a number of different scenarios for different types of tariffs (flat, dynamic) and competing energy market uses. Second, we conduct a systematic study of linear optimization models for battery control when deployed to provide flexibility to energy communities. We show that existing approaches for battery control with daily time windows have a number of important limitations in practical deployments, and we propose a number of regularization functions in the optimization to address them. Finally, we investigate the proposed method using real generation, demand, tariffs, and battery data, based on a practical case study from a large battery operator in the Netherlands. For the settings in our case study, we find that a community of 200 houses with a 330 kW wind turbine can save up to 12,874 euros per year by renting just 280 kWh of battery capacity (after subtracting battery rental costs), with the methodology applicable to a wide variety of settings and tariff types.

This article explores an approach to addressing the Close Enough Traveling Salesman Problem (CETSP). The objective is to streamline the mathematical formulation by introducing reformu-lations that approximate the Euclidean distances and simplify the objective function. Additionally, the use of convex sets in the constraint design offers computational benefits. The proposed methodology is empirically validated on real-world CETSP instances, with the aid of computational strategies such as a fragmented CPLEX-based approach. Results demonstrate its effectiveness in managing computational resources without compromising solution quality. Furthermore, the article analyzes the behavior of the proposed mathematical formulations, providing comprehensive insights into their performance.

Developing algorithms for real-life problems that perform well in practice highly depends on the availability of realistic data for testing. Obtaining real-life data for optimization problems in health care, however, is often difficult. This is especially true for any patient related optimization problems, e.g., for patient-to-room assignment, due to data privacy policies. Furthermore, obtained real-life data usually cannot be published which prohibits reproducibility of results by other researchers. Therefore, often artificially generated instances are used. We use these insights to develop a configurable instance generator for PRA with an easy-to-use graphical user interface. Configurability is in this case especially important as we observed in an extensive analysis of real-life data that, e.g., the probability distribution for patients' age and length of stay depends on the respective ward. Introduction The development of algorithms for real-world optimization problems that perform well in practice heavily relies on the availability of realistic data for testing.

A recent trend in the mathematical optimization literature is to embed trained machine learning predictors into a larger optimization model. The m ost common application is for a practitioner to train a machine learning predictor as a sur rogate for a more complicated subsystem that cannot be directly embedded into an optimiza tion model, for example, because it does not have an algebraic form or because it is non -differentiable. L opez-Flores et al. (2024) provide a review of the field.

Despite the impressive advancements in modern machine learning, achieving robustness in Domain Generalization (DG) tasks remains a significant challenge. In DG, models are expected to perform well on samples from unseen test distributions (also called domains), by learning from multiple related training distributions. Most existing approaches to this problem rely on single-valued predictions, which inherently limit their robustness. We argue that set-valued predictors could be leveraged to enhance robustness across unseen domains, while also taking into account that these sets should be as small as possible. We introduce a theoretical framework defining successful set prediction in the DG setting, focusing on meeting a predefined performance criterion across as many domains as possible, and provide theoretical insights into the conditions under which such domain generalization is achievable. We further propose a practical optimization method compatible with modern learning architectures, that balances robust performance on unseen domains with small prediction set sizes. We evaluate our approach on several real-world datasets from the WILDS benchmark, demonstrating its potential as a promising direction for robust domain generalization.