We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the function or its "hardest local alternative" to a given numerical precision. The bounds are expressed in terms of a localized and computational analogue of the modulus of continuity that is central to statistical minimax analysis. We show how the computational modulus of continuity can be explicitly calculated in concrete cases, and relates to the curvature of the function at the optimum. We also prove a superefficiency result that demonstrates it is a meaningful benchmark, acting as a computational analogue of the Fisher information in statistical estimation. The nature and practical implications of the results are demonstrated in simulations.

Guided policy search algorithms can be used to optimize complex nonlinear policies, such as deep neural networks, without directly computing policy gradients in the high-dimensional parameter space. Instead, these methods use supervised learning to train the policy to mimic a "teacher" algorithm, such as a trajectory optimizer or a trajectory-centric reinforcement learning method. Guided policy search methods provide asymptotic local convergence guarantees by construction, but it is not clear how much the policy improves within a small, finite number of iterations. We show that guided policy search algorithms can be interpreted as an approximate variant of mirror descent, where the projection onto the constraint manifold is not exact. We derive a new guided policy search algorithm that is simpler and provides appealing improvement and convergence guarantees in simplified convex and linear settings, and show that in the more general nonlinear setting, the error in the projection step can be bounded. We provide empirical results on several simulated robotic navigation and manipulation tasks that show that our method is stable and achieves similar or better performance when compared to prior guided policy search methods, with a simpler formulation and fewer hyperparameters.

Many machine learning applications involve jointly predicting multiple mutually dependent output variables. Learning to search is a family of methods where the complex decision problem is cast into a sequence of decisions via a search space. Although these methods have shown promise both in theory and in practice, implementing them has been burdensomely awkward. In this paper, we show the search space can be defined by an arbitrary imperative program, turning learning to search into a credit assignment compiler. Altogether with the algorithmic improvements for the compiler, we radically reduce the complexity of programming and the running time. We demonstrate the feasibility of our approach on multiple joint prediction tasks. In all cases, we obtain accuracies as high as alternative approaches, at drastically reduced execution and programming time.

Existing object proposal algorithms usually search for possible object regions over multiple locations and scales separately, which ignore the interdependency among different objects and deviate from the human perception procedure. To incorporate global interdependency between objects into object localization, we propose an effective Tree-structured Reinforcement Learning (Tree-RL) approach to sequentially search for objects by fully exploiting both the current observation and historical search paths. The Tree-RL approach learns multiple searching policies through maximizing the long-term reward that reflects localization accuracies over all the objects. Starting with taking the entire image as a proposal, the Tree-RL approach allows the agent to sequentially discover multiple objects via a tree-structured traversing scheme. Allowing multiple near-optimal policies, Tree-RL offers more diversity in search paths and is able to find multiple objects with a single feedforward pass. Therefore, Tree-RL can better cover different objects with various scales which is quite appealing in the context of object proposal. Experiments on PASCAL VOC 2007 and 2012 validate the effectiveness of the Tree-RL, which can achieve comparable recalls with current object proposal algorithms via much fewer candidate windows.

Given a task of predicting Y from X, a loss function L, and a set of probability distributions Γ on (X, Y), what is the optimal decision rule minimizing the worstcase expected loss over Γ? In this paper, we address this question by introducing a generalization of the maximum entropy principle. Applying this principle to sets of distributions with marginal on X constrained to be the empirical marginal, we provide a minimax interpretation of the maximum likelihood problem over generalized linear models as well as some popular regularization schemes. For quadratic and logarithmic loss functions we revisit well-known linear and logistic regression models. Moreover, for the 0-1 loss we derive a classifier which we call the minimax SVM. The minimax SVM minimizes the worst-case expected 0-1 loss over the proposed Γ by solving a tractable optimization problem. We perform several numerical experiments to show the power of the minimax SVM in outperforming the SVM.

Maximum Mean Discrepancy (MMD) is a distance on the space of probability measures which has found numerous applications in machine learning and nonparametric testing. This distance is based on the notion of embedding probabilities in a reproducing kernel Hilbert space. In this paper, we present the first known lower bounds for the estimation of MMD based on finite samples.

We show that several online combinatorial optimization problems that admit efficient no-regret algorithms become computationally hard in the sleeping setting where a subset of actions becomes unavailable in each round. Specifically, we show that the sleeping versions of these problems are at least as hard as PAC learning DNF expressions, a long standing open problem.

Several simpler estimators exist, such as Laplacian smoothing and Laplacian eigenmaps. A natural question is: can these simpler estimators perform just as well? We prove that these estimators, and more broadly all estimators given by linear transformations of the input data, are suboptimal over the class of functions with bounded variation. This extends fundamental findings of Donoho and Johnstone [12] on 1-dimensional total variation spaces to higher dimensions. The implication is that the computationally simpler methods cannot be used for such sophisticated denoising tasks, without sacrificing statistical accuracy. We also derive minimax rates for discrete Sobolev spaces over d-dimensional grids, which are, in some sense, smaller than the total variation function spaces. Indeed, these are small enough spaces that linear estimators can be optimal--and a few well-known ones are, such as Laplacian smoothing and Laplacian eigenmaps, as we show. Lastly, we investigate the adaptivity of the total variation denoiser to these smaller Sobolev function spaces.

Large language models (LLMs) are widely deployed in various downstream tasks, e.g., auto-completion, aided writing, or chat-based text generation. However, the considered output candidates of the underlying search algorithm are under-explored and under-explained. We tackle this shortcoming by proposing a tree-in-the-loop approach, where a visual representation of the beam search tree is the central component for analyzing, explaining, and adapting the generated outputs. To support these tasks, we present generAItor, a visual analytics technique, augmenting the central beam search tree with various task-specific widgets, providing targeted visualizations and interaction possibilities. Our approach allows interactions on multiple levels and offers an iterative pipeline that encompasses generating, exploring, and comparing output candidates, as well as fine-tuning the model based on adapted data. Our case study shows that our tool generates new insights in gender bias analysis beyond state-of-the-art template-based methods. Additionally, we demonstrate the applicability of our approach in a qualitative user study. Finally, we quantitatively evaluate the adaptability of the model to few samples, as occurring in text-generation use cases.

Tuning searches are pivotal in High-Performance Computing (HPC), addressing complex optimization challenges in computational applications. The complexity arises not only from finely tuning parameters within routines but also potential interdependencies among them, rendering traditional optimization methods inefficient. Instead of scrutinizing interdependencies among parameters and routines, practitioners often face the dilemma of conducting independent tuning searches for each routine, thereby overlooking interdependence, or pursuing a more resource-intensive joint search for all routines. This decision is driven by the consideration that some interdependence analysis and high-dimensional decomposition techniques in literature may be prohibitively expensive in HPC tuning searches. Our methodology adapts and refines these methods to ensure computational feasibility while maximizing performance gains in real-world scenarios. Our methodology leverages a cost-effective interdependence analysis to decide whether to merge several tuning searches into a joint search or conduct orthogonal searches. Tested on synthetic functions with varying levels of parameter interdependence, our methodology efficiently explores the search space. In comparison to Bayesian-optimization-based full independent or fully joint searches, our methodology suggested an optimized breakdown of independent and merged searches that led to final configurations up to 8% more accurate, reducing the search time by up to 95%. When applied to GPU-offloaded Real-Time Time-Dependent Density Functional Theory (RT-TDDFT), an application in computational materials science that challenges modern HPC autotuners, our methodology achieved an effective tuning search. Its adaptability and efficiency extend beyond RT-TDDFT, making it valuable for related applications in HPC.