In this paper, we address the problem of cost-sensitive hyperparameter optimization (HPO) built upon freeze-thaw Bayesian optimization (BO). Specifically, we assume a scenario where users want to early-stop the HPO process when the expected performance improvement is not satisfactory with respect to the additional computational cost. Motivated by this scenario, we introduce utility in the freezethaw framework, a function describing the trade-off between the cost and performance that can be estimated from the user's preference data. This utility function, combined with our novel acquisition function and stopping criterion, allows us to dynamically continue training the configuration that we expect to maximally improve the utility in the future, and also automatically stop the HPO process around the maximum utility. Further, we improve the sample efficiency of existing freezethaw methods with transfer learning to develop a specialized surrogate model for the cost-sensitive HPO problem. We validate our algorithm on established multifidelity HPO benchmarks and show that it outperforms all the previous freezethaw BO and transfer-BO baselines we consider, while achieving a significantly better trade-off between the cost and performance. Our code is publicly available at https://github.com/db-Lee/CFBO.

Stochastic Natural Gradient Variational Inference (NGVI) is a widely used method for approximating posterior distribution in probabilistic models. Despite its empirical success and foundational role in variational inference, its theoretical underpinnings remain limited, particularly in the case of non-conjugate likelihoods. While NGVI has been shown to be a special instance of Stochastic Mirror Descent, and recent work has provided convergence guarantees using relative smoothness and strong convexity for conjugate models, these results do not extend to the nonconjugate setting, where the variational loss becomes non-convex and harder to analyze. In this work, we focus on mean-field parameterization and advance the theoretical understanding of NGVI in three key directions. First, we derive sufficient conditions under which the variational loss satisfies relative smoothness with respect to a suitable mirror map. Second, leveraging this structure, we propose a modified NGVI algorithm incorporating non-Euclidean projections and prove its global non-asymptotic convergence to a stationary point. Finally, under additional structural assumptions about the likelihood, we uncover hidden convexity properties of the variational loss and establish fast global convergence of NGVI to a global optimum. These results provide new insights into the geometry and convergence behavior of NGVI in challenging inference settings.

Recent work in Bayesian Experiment Design (BED) has shown the value of using Deep Learning (DL) to obtain highly efficient adaptive experiment designs. In this paper, we argue that a central bottleneck of DL training for BED is belief explosion. Specifically, as an agent progresses deeper into an experiment, the effective number of realisable beliefs grows enormously, placing significant sampling burdens on offline training schemes in an effort to gather experience from all regions of belief space. We argue that choosing an appropriate inductive bias for actor/critic networks is a critical component in mitigating the effects of belief explosion and has so far been overlooked in the BED literature. We show how Graph Neural Networks are particularly well-suited for BEDDL training due to their domain permutation equivariance properties, resulting in multiple orders of magnitude improvement to sample efficiency compared to naive parameterizations.

State-space models (SSMs) are powerful probabilistic tools for modeling time-varying systems with latent dynamics. Inference in SSMs involves the estimation of latent states and parameters. In this work, we focus on parameter inference, which for SSMs is in general a very challenging problem due to the intractability of the likelihood. Recently, neural estimation methods, such as sequential neural likelihood (SNL), have shown promising results in Bayesian inference problems. In this paper, we show that SNL, when applied to the SSM setting, suffers important limitations, such as requiring a large amount of simulated samples to achieve a moderate performance, scaling poorly with sequence length, while not being amortized. We then introduce a novel inference algorithm called truncated-SNL (T-SNL), which addresses the limitations of SNL. Our algorithm is more accurate, more stable and robust during training, more scalable to longer temporal sequences, and can be amortized when new observations become available. Our experiments show that T-SNL is sample-efficient, robust, and flexible algorithm which outperforms other approaches.

While numerous works have focused on devising efficient algorithms for reinforcement learning (RL) with uniformly bounded rewards, it remains an open question whether sample or time-efficient algorithms for RL with large state-action space exist when the rewards are heavy-tailed, i.e., with only finite (1+ϵ)-th moments for some ϵ (0,1]. In this work, we address the challenge of such rewards in RL with linear function approximation.

While distributional reinforcement learning (DistRL) has been empirically effective, the question of when and why it is better than vanilla, non-distributional RL has remained unanswered. This paper explains the benefits of DistRL through the lens of small-loss bounds, which are instance-dependent bounds that scale with optimal achievable cost. Particularly, our bounds converge much faster than those from non-distributional approaches if the optimal cost is small. As warmup, we propose a distributional contextual bandit (DistCB) algorithm, which we show enjoys small-loss regret bounds and empirically outperforms the state-of-the-art on three real-world tasks. In online RL, we propose a DistRL algorithm that constructs confidence sets using maximum likelihood estimation. We prove that our algorithm enjoys novel small-loss PAC bounds in low-rank MDPs. As part of our analysis, we introduce the ℓ1 distributional eluder dimension which may be of independent interest. Then, in offline RL, we show that pessimistic DistRL enjoys small-loss PAC bounds that are novel to the offline setting and are more robust to bad single-policy coverage.

In this paper, we consider how to construct best-of-both-worlds linear bandit algorithms that achieve nearly optimal performance for both stochastic and adversarial environments. For this purpose, we show that a natural approach referred to as exploration by optimization [Lattimore and Szepesvári, 2020b] works well.

We provide the first global optimization landscape analysis of Neural Collapse-- an intriguing empirical phenomenon that arises in the last-layer classifiers and features of neural networks during the terminal phase of training. As recently reported in [1], this phenomenon implies that (i) the class means and the last-layer classifiers all collapse to the vertices of a Simplex Equiangular Tight Frame (ETF) up to scaling, and (ii) cross-example within-class variability of last-layer activations collapses to zero. We study the problem based on a simplified unconstrained feature model, which isolates the topmost layers from the classifier of the neural network. In this context, we show that the classical cross-entropy loss with weight decay has a benign global landscape, in the sense that the only global minimizers are the Simplex ETFs while all other critical points are strict saddles whose Hessian exhibit negative curvature directions. Our analysis of the simplified model not only explains what kind of features are learned in the last layer, but also shows why they can be efficiently optimized, matching the empirical observations in practical deep network architectures. These findings provide important practical implications. As an example, our experiments demonstrate that one may set the feature dimension equal to the number of classes and fix the last-layer classifier to be a Simplex ETF for network training, which reduces memory cost by over 20% on ResNet18 without sacrificing the generalization performance.