Multi-objective optimization is a class of optimization problems with multiple conflicting objectives. We study offline optimization of multi-objective policies from data collected by a previously deployed policy. We propose a pessimistic estimator for policy values that can be easily plugged into existing formulas for hypervolume computation and optimized. The estimator is based on inverse propensity scores (IPS), and improves upon a naive IPS estimator in both theory and experiments. Our analysis is general, and applies beyond our IPS estimators and methods for optimizing them.

Large models training is plagued by the intense compute cost and limited hardware memory. A practical solution is low-precision representation but is troubled by loss in numerical accuracy and unstable training rendering the model less useful. We argue that low-precision floating points can perform well provided the error is properly compensated at the critical locations in the training process. We propose Collage which utilizes multi-component float representation in low-precision to accurately perform operations with numerical errors accounted. To understand the impact of imprecision to training, we propose a simple and novel metric which tracks the lost information during training as well as differentiates various precision strategies. Our method works with commonly used low-precision such as half-precision ($16$-bit floating points) and can be naturally extended to work with even lower precision such as $8$-bit. Experimental results show that pre-training using Collage removes the requirement of using $32$-bit floating-point copies of the model and attains similar/better training performance compared to $(16, 32)$-bit mixed-precision strategy, with up to $3.7\times$ speedup and $\sim 15\%$ to $23\%$ less memory usage in practice. The code is available at https://github.com/amazon-science/collage.

As the world's largest retailer, Walmart's core mission is to save people money so they can live better. We call the strategy we use to accomplish this goal our Every Day Low Price strategy. By keeping operational expenses as low as possible, we can continually apply a downward pressure on our prices, in turn increasing the amount of traffic, and ultimately, sales within our stores. In this paper, we apply Machine Learning (ML) algorithms and Operations Research techniques for forecasting and optimization to build a new price recommendation system, which improves our ability to generate price recommendations accurately and automatically. Comprised of a demand forecasting step, two optimizations, and causal inference analysis, our system was evaluated in the form of forecast backtests and live pricing experiments, both of which suggested that our approach was more effective than the current rule-based pricing system.