We study the contextual continuum bandits problem, where the learner sequentially receives a side information vector and has to choose an action in a convex set, minimizing a function associated to the context. The goal is to minimize all the underlying functions for the received contexts, leading to a dynamic (contextual) notion of regret, which is stronger than the standard static regret. Assuming that the objective functions are H\"older with respect to the contexts, we demonstrate that any algorithm achieving a sub-linear static regret can be extended to achieve a sub-linear dynamic regret. We further study the case of strongly convex and smooth functions when the observations are noisy. Inspired by the interior point method and employing self-concordant barriers, we propose an algorithm achieving a sub-linear dynamic regret. Lastly, we present a minimax lower bound, implying two key facts. First, no algorithm can achieve sub-linear dynamic regret over functions that are not continuous with respect to the context. Second, for strongly convex and smooth functions, the algorithm that we propose achieves, up to a logarithmic factor, the minimax optimal rate of dynamic regret as a function of the number of queries.

Gradient-free prompt optimization methods have made significant strides in enhancing the performance of closed-source Large Language Models (LLMs) across a wide range of tasks. However, existing approaches make light of the importance of high-quality prompt initialization and the identification of effective optimization directions, thus resulting in substantial optimization steps to obtain satisfactory performance. In this light, we aim to accelerate prompt optimization process to tackle the challenge of low convergence rate. We propose a dual-phase approach which starts with generating high-quality initial prompts by adopting a well-designed meta-instruction to delve into task-specific information, and iteratively optimize the prompts at the sentence level, leveraging previous tuning experience to expand prompt candidates and accept effective ones. Extensive experiments on eight datasets demonstrate the effectiveness of our proposed method, achieving a consistent accuracy gain over baselines with less than five optimization steps.

Many combinatorial optimization problems that face diminishing returns can be stated in terms of a submodular function under given set of constraints [7]. The maximization of a non-monotone submodular function even without constraints includes the classical maximum cut problem in graphs and is therefore an NP-hard combinatorial optimization problem that cannot be solved in polynomial time unless P = N P but different types of approximation algorithms are available [2]. Monotone submodular functions play a special role in the area of optimization as they capture import coverage and influence maximization problems in networks. The maximization of monotone submodular functions is NP-hard even for the case of simple constraint that limits the number of elements that can be chosen, but greedy algorithms have shown to obtain best possible approximation guarantees for different types of constraints [7, 8]. At best, one can hope to develop a method that can provide an α-approximation in polynomial time, i.e., a solution with a value of at least α f(x

Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions for efficiently solving the Quadratic Assignment Problem (QAPs), which stands as a formidable challenge in combinatorial optimization. While many instances of simpler problems admit fully polynomial-time approximate solution (FPTAS), QAP is shown to be strongly NP-hard. Even finding a FPTAS for QAP is difficult, in the sense that the existence of a FPTAS implies $P = NP$. Current research on QAPs suffer from limited scale and computational inefficiency. To attack the aforementioned issues, we here propose the first solution of its kind for QAP in the learn-to-improve category. This work encodes facility and location nodes separately, instead of forming computationally intensive association graphs prevalent in current approaches. This design choice enables scalability to larger problem sizes. Furthermore, a \textbf{S}olution \textbf{AW}are \textbf{T}ransformer (SAWT) architecture integrates the incumbent solution matrix with the attention score to effectively capture higher-order information of the QAPs. Our model's effectiveness is validated through extensive experiments on self-generated QAP instances of varying sizes and the QAPLIB benchmark.

We revisit the classical problem of multiclass classification with bandit feedback (Kakade, Shalev-Shwartz and Tewari, 2008), where each input classifies to one of $K$ possible labels and feedback is restricted to whether the predicted label is correct or not. Our primary inquiry is with regard to the dependency on the number of labels $K$, and whether $T$-step regret bounds in this setting can be improved beyond the $\smash{\sqrt{KT}}$ dependence exhibited by existing algorithms. Our main contribution is in showing that the minimax regret of bandit multiclass is in fact more nuanced, and is of the form $\smash{\widetilde{\Theta}\left(\min \left\{|H| + \sqrt{T}, \sqrt{KT \log |H|} \right\} \right) }$, where $H$ is the underlying (finite) hypothesis class. In particular, we present a new bandit classification algorithm that guarantees regret $\smash{\widetilde{O}(|H|+\sqrt{T})}$, improving over classical algorithms for moderately-sized hypothesis classes, and give a matching lower bound establishing tightness of the upper bounds (up to log-factors) in all parameter regimes.

The critical inquiry pervading the realm of Philosophy, and perhaps extending its influence across all Humanities disciplines, revolves around the intricacies of morality and normativity. Surprisingly, in recent years, this thematic thread has woven its way into an unexpected domain, one not conventionally associated with pondering "what ought to be": the field of artificial intelligence (AI) research. Central to morality and AI, we find "alignment", a problem related to the challenges of expressing human goals and values in a manner that artificial systems can follow without leading to unwanted adversarial effects. More explicitly and with our current paradigm of AI development in mind, we can think of alignment as teaching human values to non-anthropomorphic entities trained through opaque, gradient-based learning techniques. This work addresses alignment as a technical-philosophical problem that requires solid philosophical foundations and practical implementations that bring normative theory to AI system development. To accomplish this, we propose two sets of necessary and sufficient conditions that, we argue, should be considered in any alignment process. While necessary conditions serve as metaphysical and metaethical roots that pertain to the permissibility of alignment, sufficient conditions establish a blueprint for aligning AI systems under a learning-based paradigm. After laying such foundations, we present implementations of this approach by using state-of-the-art techniques and methods for aligning general-purpose language systems. We call this framework Dynamic Normativity. Its central thesis is that any alignment process under a learning paradigm that cannot fulfill its necessary and sufficient conditions will fail in producing aligned systems.

To make accurate predictions, understand mechanisms, and design interventions in systems of many variables, we wish to learn causal graphs from large scale data. Unfortunately the space of all possible causal graphs is enormous so scalably and accurately searching for the best fit to the data is a challenge. In principle we could substantially decrease the search space, or learn the graph entirely, by testing the conditional independence of variables. However, deciding if two variables are adjacent in a causal graph may require an exponential number of tests. Here we build a scalable and flexible method to evaluate if two variables are adjacent in a causal graph, the Differentiable Adjacency Test (DAT). DAT replaces an exponential number of tests with a provably equivalent relaxed problem. It then solves this problem by training two neural networks. We build a graph learning method based on DAT, DAT-Graph, that can also learn from data with interventions. DAT-Graph can learn graphs of 1000 variables with state of the art accuracy. Using the graph learned by DAT-Graph, we also build models that make much more accurate predictions of the effects of interventions on large scale RNA sequencing data.

Graph neural networks (GNNs) have emerged as a powerful tool for solving combinatorial optimization problems (COPs), exhibiting state-of-the-art performance in both graph-structured and non-graph-structured domains. However, existing approaches lack a unified framework capable of addressing a wide range of COPs. After presenting a summary of representative COPs and a brief review of recent advancements in GNNs for solving COPs, this paper proposes a unified framework for solving COPs based on GNNs, including graph representation of COPs, equivalent conversion of non-graph structured COPs to graph-structured COPs, graph decomposition, and graph simplification. The proposed framework leverages the ability of GNNs to effectively capture the relational information and extract features from the graph representation of COPs, offering a generic solution to COPs that can address the limitations of state-of-the-art in solving non-graph-structured and highly complex graph-structured COPs.

GNNs are powerful models based on node representation learning that perform particularly well in many machine learning problems related to graphs. The major obstacle to the deployment of GNNs is mostly a problem of societal acceptability and trustworthiness, properties which require making explicit the internal functioning of such models. Here, we propose to mine activation rules in the hidden layers to understand how the GNNs perceive the world. The problem is not to discover activation rules that are individually highly discriminating for an output of the model. Instead, the challenge is to provide a small set of rules that cover all input graphs. To this end, we introduce the subjective activation pattern domain. We define an effective and principled algorithm to enumerate activations rules in each hidden layer. The proposed approach for quantifying the interest of these rules is rooted in information theory and is able to account for background knowledge on the input graph data. The activation rules can then be redescribed thanks to pattern languages involving interpretable features. We show that the activation rules provide insights on the characteristics used by the GNN to classify the graphs. Especially, this allows to identify the hidden features built by the GNN through its different layers. Also, these rules can subsequently be used for explaining GNN decisions. Experiments on both synthetic and real-life datasets show highly competitive performance, with up to 200% improvement in fidelity on explaining graph classification over the SOTA methods.

When a robot autonomously performs a complex task, it frequently must balance competing objectives while maintaining safety. This becomes more difficult in uncertain environments with stochastic outcomes. Enhancing transparency in the robot's behavior and aligning with user preferences are also crucial. This paper introduces a novel framework for multi-objective reinforcement learning that ensures safe task execution, optimizes trade-offs between objectives, and adheres to user preferences. The framework has two main layers: a multi-objective task planner and a high-level selector. The planning layer generates a set of optimal trade-off plans that guarantee satisfaction of a temporal logic task. The selector uses active inference to decide which generated plan best complies with user preferences and aids learning. Operating iteratively, the framework updates a parameterized learning model based on collected data. Case studies and benchmarks on both manipulation and mobile robots show that our framework outperforms other methods and (i) learns multiple optimal trade-offs, (ii) adheres to a user preference, and (iii) allows the user to adjust the balance between (i) and (ii).