The first algorithm for the Linear Quadratic (LQ) control problem with an unknown system model, featuring a regret of $\mathcal{O}(\sqrt{T})$, was introduced by Abbasi-Yadkori and Szepesv\'ari (2011). Recognizing the computational complexity of this algorithm, subsequent efforts (see Cohen et al. (2019), Mania et al. (2019), Faradonbeh et al. (2020a), and Kargin et al.(2022)) have been dedicated to proposing algorithms that are computationally tractable while preserving this order of regret. Although successful, the existing works in the literature lack a fully adaptive exploration-exploitation trade-off adjustment and require a user-defined value, which can lead to overall regret bound growth with some factors. In this work, noticing this gap, we propose the first fully adaptive algorithm that controls the number of policy updates (i.e., tunes the exploration-exploitation trade-off) and optimizes the upper-bound of regret adaptively. Our proposed algorithm builds on the SDP-based approach of Cohen et al. (2019) and relaxes its need for a horizon-dependant warm-up phase by appropriately tuning the regularization parameter and adding an adaptive input perturbation. We further show that through careful exploration-exploitation trade-off adjustment there is no need to commit to the widely-used notion of strong sequential stability, which is restrictive and can introduce complexities in initialization.
Cutaneous squamous cell cancer (cSCC) is the second most common skin cancer in the US. It is diagnosed by manual multi-class tumor grading using a tissue whole slide image (WSI), which is subjective and suffers from inter-pathologist variability. We propose an automated weakly-supervised grading approach for cSCC WSIs that is trained using WSI-level grade and does not require fine-grained tumor annotations. The proposed model, RACR-MIL, transforms each WSI into a bag of tiled patches and leverages attention-based multiple-instance learning to assign a WSI-level grade. We propose three key innovations to address general as well as cSCC-specific challenges in tumor grading. First, we leverage spatial and semantic proximity to define a WSI graph that encodes both local and non-local dependencies between tumor regions and leverage graph attention convolution to derive contextual patch features. Second, we introduce a novel ordinal ranking constraint on the patch attention network to ensure that higher-grade tumor regions are assigned higher attention. Third, we use tumor depth as an auxiliary task to improve grade classification in a multitask learning framework. RACR-MIL achieves 2-9% improvement in grade classification over existing weakly-supervised approaches on a dataset of 718 cSCC tissue images and localizes the tumor better. The model achieves 5-20% higher accuracy in difficult-to-classify high-risk grade classes and is robust to class imbalance.
To promote new scientific discoveries from complex data sets, feature importance inference has been a long-standing statistical problem. Instead of testing for parameters that are only interpretable for specific models, there has been increasing interest in model-agnostic methods, often in the form of feature occlusion or leave-one-covariate-out (LOCO) inference. Existing approaches often make distributional assumptions, which can be difficult to verify in practice, or require model refitting and data splitting, which are computationally intensive and lead to losses in power. In this work, we develop a novel, mostly model-agnostic and distribution-free inference framework for feature importance that is computationally efficient and statistically powerful. Our approach is fast as we avoid model refitting by leveraging a form of random observation and feature subsampling called minipatch ensembles; this approach also improves statistical power by avoiding data splitting. Our framework can be applied on tabular data and with any machine learning algorithm, together with minipatch ensembles, for regression and classification tasks. Despite the dependencies induced by using minipatch ensembles, we show that our approach provides asymptotic coverage for the feature importance score of any model under mild assumptions. Finally, our same procedure can also be leveraged to provide valid confidence intervals for predictions, hence providing fast, simultaneous quantification of the uncertainty of both predictions and feature importance. We validate our intervals on a series of synthetic and real data examples, including non-linear settings, showing that our approach detects the correct important features and exhibits many computational and statistical advantages over existing methods.