We study bandit learning in matching markets with two-sided reward uncertainty, extending prior research primarily focused on single-sided uncertainty. Leveraging the concept of `super-stability' from Irving (1994), we demonstrate the advantage of the Extended Gale-Shapley (GS) algorithm over the standard GS algorithm in achieving true stable matchings under incomplete information. By employing the Extended GS algorithm, our centralized algorithm attains a logarithmic pessimal stable regret dependent on an instance-dependent admissible gap parameter. This algorithm is further adapted to a decentralized setting with a constant regret increase. Finally, we establish a novel centralized instance-dependent lower bound for binary stable regret, elucidating the roles of the admissible gap and super-stable matching in characterizing the complexity of stable matching with bandit feedback.

We develop a Bayesian approach to predict a continuous or binary outcome from data that are collected from multiple sources with a multi-way (i.e.. multidimensional tensor) structure. As a motivating example we consider molecular data from multiple 'omics sources, each measured over multiple developmental time points, as predictors of early-life iron deficiency (ID) in a rhesus monkey model. We use a linear model with a low-rank structure on the coefficients to capture multi-way dependence and model the variance of the coefficients separately across each source to infer their relative contributions. Conjugate priors facilitate an efficient Gibbs sampling algorithm for posterior inference, assuming a continuous outcome with normal errors or a binary outcome with a probit link. Simulations demonstrate that our model performs as expected in terms of misclassification rates and correlation of estimated coefficients with true coefficients, with large gains in performance by incorporating multi-way structure and modest gains when accounting for differing signal sizes across the different sources. Moreover, it provides robust classification of ID monkeys for our motivating application. Software in the form of R code is available at https://github.com/BiostatsKim/BayesMSMW .

The Conformer-Kernel (CK) model [Mitra et al., 2020] builds upon the Transformer-Kernel (TK) [Hofstätter et al., 2019] architecture, that demonstrated strong competitive performance compared to BERTbased [Devlin et al., 2019] ranking methods, but notably at a fraction of the compute and GPU memory cost, at the TREC 2019 Deep Learning track [Craswell et al., 2020b]. Notwithstanding these strong results, the TK model suffers from two clear deficiencies. Firstly, because the TK model employs stacked Transformers for query and document encoding, it is challenging to incorporate long body text into this model as the GPU memory requirement of Transformers' self-attention layers grows quadratically with respect to input sequence length. So, for example, to increase the limit on the maximum input sequence length by 4 from 128 to 512 we would require 16 more GPU memory for each of the self-attention layers in the model. Considering that documents can contain thousands of terms, this limits the model to inspecting only a subset of the document text which may have negative implications, such as poorer retrieval quality and under-retrieval of longer documents [Hofstätter et al., 2020].