Large Language Models and multi-agent systems have shown promise in decomposing complex tasks, yet they struggle with long-horizon reasoning tasks and escalating computation cost. This work introduces a hierarchical multi-agent architecture that distributes reasoning across a 64*64 grid of lightweight agents, supported by a selective oracle. A spatial curriculum progressively expands the operational region of the grid, ensuring that agents master easier central tasks before tackling harder peripheral ones. To improve reliability, the system integrates Negative Log-Likelihood as a measure of confidence, allowing the curriculum to prioritize regions where agents are both accurate and well calibrated. A Thompson Sampling curriculum manager adaptively chooses training zones based on competence and NLL-driven reward signals. We evaluate the approach on a spatially grounded Tower of Hanoi benchmark, which mirrors the long-horizon structure of many robotic manipulation and planning tasks. Results demonstrate improved stability, reduced oracle usage, and stronger long-range reasoning from distributed agent cooperation.

When should an autonomous agent commit resources to a task? We introduce the Agent Capability Problem (ACP), a framework for predicting whether an agent can solve a problem under resource constraints. Rather than relying on empirical heuristics, ACP frames problem-solving as information acquisition: an agent requires $\Itotal$ bits to identify a solution and gains $\Istep$ bits per action at cost $\Cstep$, yielding an effective cost $\Ceff = (\Itotal/\Istep), \Cstep$ that predicts resource requirements before search. We prove that $\Ceff$ lower-bounds expected cost and provide tight probabilistic upper bounds. Experimental validation shows that ACP predictions closely track actual agent performance, consistently bounding search effort while improving efficiency over greedy and random strategies. The framework generalizes across LLM-based and agentic workflows, linking principles from active learning, Bayesian optimization, and reinforcement learning through a unified information-theoretic lens. \

Modern high-frequency trading (HFT) environments are characterized by sudden price spikes that present both risk and opportunity, but conventional financial models often fail to capture the required fine temporal structure. Spiking Neural Networks (SNNs) offer a biologically inspired framework well-suited to these challenges due to their natural ability to process discrete events and preserve millisecond-scale timing. This work investigates the application of SNNs to high-frequency price-spike forecasting, enhancing performance via robust hyperparameter tuning with Bayesian Optimization (BO). This work converts high-frequency stock data into spike trains and evaluates three architectures: an established unsupervised STDP-trained SNN, a novel SNN with explicit inhibitory competition, and a supervised backpropagation network. BO was driven by a novel objective, Penalized Spike Accuracy (PSA), designed to ensure a network's predicted price spike rate aligns with the empirical rate of price events. Simulated trading demonstrated that models optimized with PSA consistently outperformed their Spike Accuracy (SA)-tuned counterparts and baselines. Specifically, the extended SNN model with PSA achieved the highest cumulative return (76.8%) in simple backtesting, significantly surpassing the supervised alternative (42.54% return). These results validate the potential of spiking networks, when robustly tuned with task-specific objectives, for effective price spike forecasting in HFT.

In this work we investigate the relationship between kernel regularity and algorithmic performance in the bandit optimization of RKHS functions. While reproducing kernel Hilbert space (RKHS) methods traditionally rely on global kernel regressors, it is also common to use a smoothness-based approach that exploits local approximations. We show that these perspectives are deeply connected through the spectral properties of isotropic kernels. In particular, we characterize the Fourier spectra of the Matérn, square-exponential, rational-quadratic, $\gamma$-exponential, piecewise-polynomial, and Dirichlet kernels, and show that the decay rate determines asymptotic regret from both viewpoints. For kernelized bandit algorithms, spectral decay yields upper bounds on the maximum information gain, governing worst-case regret, while for smoothness-based methods, the same decay rates establish Hölder space embeddings and Besov space norm-equivalences, enabling local continuity analysis. These connections show that kernel-based and locally adaptive algorithms can be analyzed within a unified framework. This allows us to derive explicit regret bounds for each kernel family, obtaining novel results in several cases and providing improved analysis for others. Furthermore, we analyze LP-GP-UCB, an algorithm that combines both approaches, augmenting global Gaussian process surrogates with local polynomial estimators. While the hybrid approach does not uniformly dominate specialized methods, it achieves order-optimality across multiple kernel families.

We study the calibration of Gaussian process (GP) predictive distributions in the interpolation setting from a design-marginal perspective. Conditioning on the data and averaging over a design measure \mu, we formalize \mu-coverage for central intervals and \mu-probabilistic calibration through randomized probability integral transforms. We introduce two methods. cps-gp adapts conformal predictive systems to GP interpolation using standardized leave-one-out residuals, yielding stepwise predictive distributions with finite-sample marginal calibration. bcr-gp retains the GP posterior mean and replaces the Gaussian residual by a generalized normal model fitted to cross-validated standardized residuals. A Bayesian selection rule-based either on a posterior upper quantile of the variance for conservative prediction or on a cross-posterior Kolmogorov-Smirnov criterion for probabilistic calibration-controls dispersion and tail behavior while producing smooth predictive distributions suitable for sequential design. Numerical experiments on benchmark functions compare cps-gp, bcr-gp, Jackknife+ for GPs, and the full conformal Gaussian process, using calibration metrics (coverage, Kolmogorov-Smirnov, integral absolute error) and accuracy or sharpness through the scaled continuous ranked probability score.

Timely assessment of current conditions is essential especially for small, open economies such as Singapore, where external shocks transmit rapidly to domestic activity. We develop a real-time nowcasting framework for quarterly GDP growth using a high-dimensional panel of approximately 70 indicators, encompassing economic and financial indicators over 1990Q1-2023Q2. The analysis covers penalized regressions, dimensionality-reduction methods, ensemble learning algorithms, and neural architectures, benchmarked against a Random Walk, an AR(3), and a Dynamic Factor Model. The pipeline preserves temporal ordering through an expanding-window walk-forward design with Bayesian hyperparameter optimization, and uses moving block-bootstrap procedures both to construct prediction intervals and to obtain confidence bands for feature-importance measures. It adopts model-specific and XAI-based explainability tools. A Model Confidence Set procedure identifies statistically superior learners, which are then combined through simple, weighted, and exponentially weighted schemes; the resulting time-varying weights provide an interpretable representation of model contributions. Predictive ability is assessed via Giacomini-White tests. Empirical results show that penalized regressions, dimensionality-reduction models, and GRU networks consistently outperform all benchmarks, with RMSFE reductions of roughly 40-60%; aggregation delivers further gains. Feature-attribution methods highlight industrial production, external trade, and labor-market indicators as dominant drivers of Singapore's short-run growth dynamics.

High-dimensional spaces have challenged Bayesian optimization (BO). Existing methods aim to overcome this so-called curse of dimensionality by carefully encoding structural assumptions, from locality to sparsity to smoothness, into the optimization procedure. Surprisingly, we demonstrate that these approaches are outperformed by arguably the simplest method imaginable: Bayesian linear regression. After applying a geometric transformation to avoid boundary-seeking behavior, Gaussian processes with linear kernels match state-of-the-art performance on tasks with 60- to 6,000-dimensional search spaces. Linear models offer numerous advantages over their non-parametric counterparts: they afford closed-form sampling and their computation scales linearly with data, a fact we exploit on molecular optimization tasks with > 20,000 observations. Coupled with empirical analyses, our results suggest the need to depart from past intuitions about BO methods in high-dimensional spaces.

Recent work on autonomous scientific discovery has leveraged LLM-based agents to integrate problem specification, experiment planning, and execution into end-to-end systems. However, these frameworks are often confined to narrow application domains, offer limited real-time interaction with researchers, and lack principled mechanisms for determining when to halt exploration, resulting in inefficiencies, reproducibility challenges, and under-utilized human expertise. To address these gaps, we propose \textit{SelfAI}, a general multi-agent platform that combines a User Agent for translating high-level research objectives into standardized experimental configurations, a Cognitive Agent powered by LLMs with optimal stopping criteria to iteratively refine hyperparameter searches, and an Experiment Manager responsible for orchestrating parallel, fault-tolerant training workflows across heterogeneous hardware while maintaining a structured knowledge base for continuous feedback. We further introduce two novel evaluation metrics, Score and $\text{AUP}_D$, to quantify discovery efficiency and search diversity. Across regression, NLP, computer vision, scientific computing, medical imaging, and drug discovery benchmarks, SelfAI consistently achieves strong performance and reduces redundant trials compared to classical Bayesian optimization and LLM-based baselines, while enabling seamless interaction with human researchers.

The optimal assignment of Large Language Models (LLMs) to specialized roles in multi-agent systems is a significant challenge, defined by a vast combinatorial search space, expensive black-box evaluations, and an inherent trade-off between performance and cost. Current optimization methods focus on single-agent settings and lack a principled framework for this multi-agent, multi-objective problem. This thesis introduces MALBO (Multi-Agent LLM Bayesian Optimization), a systematic framework designed to automate the efficient composition of LLM-based agent teams. We formalize the assignment challenge as a multi-objective optimization problem, aiming to identify the Pareto front of configurations between task accuracy and inference cost. The methodology employs multi-objective Bayesian Optimization (MOBO) with independent Gaussian Process surrogate models. By searching over a continuous feature-space representation of the LLMs, this approach performs a sample-efficient exploration guided by the expected hypervolume improvement. The primary contribution is a principled and automated methodology that yields a Pareto front of optimal team configurations. Our results demonstrate that the Bayesian optimization phase, compared to an initial random search, maintained a comparable average performance while reducing the average configuration cost by over 45%. Furthermore, MALBO identified specialized, heterogeneous teams that achieve cost reductions of up to 65.8% compared to homogeneous baselines, all while maintaining maximum performance. The framework thus provides a data-driven tool for deploying cost-effective and highly specialized multi-agent AI systems.

We introduce active generation of Pareto sets (A-GPS), a new framework for online discrete black-box multi-objective optimization (MOO). A-GPS learns a generative model of the Pareto set that supports a-posteriori conditioning on user preferences. The method employs a class probability estimator (CPE) to predict non-dominance relations and to condition the generative model toward high-performing regions of the search space. We also show that this non-dominance CPE implicitly estimates the probability of hypervolume improvement (PHVI). To incorporate subjective trade-offs, A-GPS introduces preference direction vectors that encode user-specified preferences in objective space. At each iteration, the model is updated using both Pareto membership and alignment with these preference directions, producing an amortized generative model capable of sampling across the Pareto front without retraining. The result is a simple yet powerful approach that achieves high-quality Pareto set approximations, avoids explicit hypervolume computation, and flexibly captures user preferences. Empirical results on synthetic benchmarks and protein design tasks demonstrate strong sample efficiency and effective preference incorporation.

Bayesian optimization is a natural candidate for the engineering of antibody therapeutic properties, which is often iterative and expensive. However, finding the optimal choice of surrogate model for optimization over the highly structured antibody space is difficult, and may differ depending on the property being optimized. Moreover, to the best of our knowledge, no prior works have attempted to incorporate structural information into antibody Bayesian optimization. In this work, we explore different approaches to incorporating structural information into Bayesian optimization, and compare them to a variety of sequence-only approaches on two different antibody properties, binding affinity and stability. In addition, we propose the use of a protein language model-based ``soft constraint,'' which helps guide the optimization to promising regions of the space. We find that certain types of structural information improve data efficiency in early optimization rounds for stability, but have equivalent peak performance. Moreover, when incorporating the protein language model soft constraint we find that the data efficiency gap is diminished for affinity and eliminated for stability, resulting in sequence-only methods that match the performance of structure-based methods, raising questions about the necessity of structure in Bayesian optimization for antibodies.

Optimizing high-dimensional black-box functions under black-box constraints is a pervasive task in a wide range of scientific and engineering problems. These problems are typically harder than unconstrained problems due to hard-to-find feasible regions. While Bayesian optimization (BO) methods have been developed to solve such problems, they often struggle with the curse of dimensionality. Recently, generative model-based approaches have emerged as a promising alternative for constrained optimization. However, they suffer from poor scalability and are vulnerable to mode collapse, particularly when the target distribution is highly multi-modal. In this paper, we propose a new framework to overcome these challenges. Our method iterates through two stages. First, we train flow-based models to capture the data distribution and surrogate models that predict both function values and constraint violations with uncertainty quantification. Second, we cast the candidate selection problem as a posterior inference problem to effectively search for promising candidates that have high objective values while not violating the constraints. During posterior inference, we find that the posterior distribution is highly multi-modal and has a large plateau due to constraints, especially when constraint feedback is given as binary indicators of feasibility. To mitigate this issue, we amortize the sampling from the posterior distribution in the latent space of flow-based models, which is much smoother than that in the data space. We empirically demonstrate that our method achieves superior performance on various synthetic and real-world constrained black-box optimization tasks. Our code is publicly available \href{this https URL}{here}.

With the rise of different language model architecture, fine-tuning is becoming even more important for down stream tasks Model gets messy, finding proper hyperparameters for fine-tuning. Although BO has been tried for hyperparameter tuning, most of the existing methods are oblivious to the fact that BO relies on careful choices of acquisition functions, which are essential components of BO that guide how much to explore versus exploit during the optimization process; Different acquisition functions have different levels of sensitivity towards training loss and validation performance; existing methods often just apply an acquisition function no matter if the training and validation performance are sensitive to the acquisition function or not. This work introduces{Bilevel - BO - SWA}, a model fusion approach coupled with a bilevel BO strategy to improve the fine - tunning of large language models. Our work on mixture of acquisition functions like EI and UCB into nested opt loops, where inner loop perform minimization of training loss while outer loops optimized w.r.t. val metric. Experiments on GLUE tasks using RoBERTA - base show that when using EI and UCB, there is an improvement in generalization, and fine - tuning can be improved by up to 2.7%.

Given a large pool of unlabelled data and a smaller amount of labels, prediction-powered inference (PPI) leverages machine learning predictions to increase the statistical efficiency of standard confidence interval procedures based solely on labelled data, while preserving their fixed-time validity. In this paper, we extend the PPI framework to the sequential setting, where labelled and unlabelled datasets grow over time. Exploiting Ville's inequality and the method of mixtures, we propose prediction-powered confidence sequence procedures that are valid uniformly over time and naturally accommodate prior knowledge on the quality of the predictions to further boost efficiency. We carefully illustrate the design choices behind our method and demonstrate its effectiveness in real and synthetic examples.