We consider a stochastic inventory control problem under censored demand, lost sales, and positive lead times. This is a fundamental problem in inventory management, with significant literature establishing near optimality of a simple class of policies called “base-stock policies” as well as the convexity of long-run average cost under those policies. We consider a relatively less studied problem of designing a learning algorithm for this problem when the underlying demand distribution is unknown. The goal is to bound the regret of the algorithm when compared with the best base-stock policy. Our main contribution is a learning algorithm with a regret bound of [Formula: see text] for the inventory control problem. Here, [Formula: see text] is the fixed and known lead time, and D is an unknown parameter of the demand distribution described roughly as the expected number of time steps needed to generate enough demand to deplete one unit of inventory. Notably, our regret bounds depend linearly on L, which significantly improves the previously best-known regret bounds for this problem where the dependence on L was exponential. Our techniques utilize the convexity of the long-run average cost and a newly derived bound on the “bias” of base-stock policies to establish an almost black box connection between the problem of learning in Markov decision processes (MDPs) with these properties and the stochastic convex bandit problem. The techniques presented here may be of independent interest for other settings that involve large structured MDPs but with convex asymptotic average cost functions.
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Misspecification in Prediction Problems and Robustness via Improper Learning
We study probabilistic prediction games when the underlying model is misspecified, investigating the consequences of predicting using an incorrect parametric model. We show that for a broad class of loss functions and parametric families of distributions, the regret of playing a ``proper'' predictor--one from the putative model class--relative to the best predictor in the same model class has lower bound scaling at least as sqrt(c n), where c is a measure of the model misspecification to the true distribution in terms of total variation distance. In contrast, using an aggregation-based (improper) learner, one can obtain regret d log n for any underlying generating distribution, where d is the dimension of the parameter; we exhibit instances in which this is unimprovable even over the family of all learners that may play distributions in the convex hull of the parametric family. These results suggest that simple strategies for aggregating multiple learners together should be more robust, and several experiments conform to this hypothesis.
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- NSF-PAR ID:
- 10275097
- Date Published:
- Journal Name:
- AISTATS
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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The Study on U.S. Parents’ Divisions of Labor During COVID-19 (SPDLC) collects longitudinal survey data from partnered U.S. parents that can be used to assess changes in parents’ divisions of domestic labor, divisions of paid labor, and well-being throughout and after the COVID-19 pandemic. The goal of SPDLC is to understand both the short- and long-term impacts of the pandemic for the gendered division of labor, work-family issues, and broader patterns of gender inequality.
Survey data for this study is collected using Prolifc (www.prolific.co), an opt-in online platform designed to facilitate scientific research. The sample is comprised U.S. adults who were residing with a romantic partner and at least one biological child (at the time of entry into the study). In each survey, parents answer questions about both themselves and their partners. Wave 1 of SPDLC was conducted in April 2020, and parents who participated in Wave 1 were asked about their division of labor both prior to (i.e., early March 2020) and one month after the pandemic began. Wave 2 of SPDLC was collected in November 2020. Parents who participated in Wave 1 were invited to participate again in Wave 2, and a new cohort of parents was also recruited to participate in the Wave 2 survey. Wave 3 of SPDLC was collected in October 2021. Parents who participated in either of the first two waves were invited to participate again in Wave 3, and another new cohort of parents was also recruited to participate in the Wave 3 survey. This research design (follow-up survey of panelists and new cross-section of parents at each wave) will continue through 2024, culminating in six waves of data spanning the period from March 2020 through October 2024. An estimated total of approximately 6,500 parents will be surveyed at least once throughout the duration of the study.
SPDLC data will be released to the public two years after data is collected; Waves 1 and 2 are currently publicly available. Wave 3 will be publicly available in October 2023, with subsequent waves becoming available yearly. Data will be available to download in both SPSS (.sav) and Stata (.dta) formats, and the following data files will be available: (1) a data file for each individual wave, which contains responses from all participants in that wave of data collection, (2) a longitudinal panel data file, which contains longitudinal follow-up data from all available waves, and (3) a repeated cross-section data file, which contains the repeated cross-section data (from new respondents at each wave) from all available waves. Codebooks for each survey wave and a detailed user guide describing the data are also available. Response Rates: Of the 1,157 parents who participated in Wave 1, 828 (72%) also participated in the Wave 2 study. Presence of Common Scales: The following established scales are included in the survey:- Self-Efficacy, adapted from Pearlin's mastery scale (Pearlin et al., 1981) and the Rosenberg self-esteem scale (Rosenberg, 2015) and taken from the American Changing Lives Survey
- Communication with Partner, taken from the Marriage and Relationship Survey (Lichter & Carmalt, 2009)
- Gender Attitudes, taken from the National Survey of Families and Households (Sweet & Bumpass, 1996)
- Depressive Symptoms (CES-D-10)
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The second wave of the SPDLC was fielded in November 2020 in two stages. In the first stage, all parents who participated in W1 of the SPDLC and who continued to reside in the United States were re-contacted and asked to participate in a follow-up survey. The W2 survey was posted on Prolific, and messages were sent via Prolific’s messaging system to all previous participants. Multiple follow-up messages were sent in an attempt to increase response rates to the follow-up survey. Of the 1,157 respondents who completed the W1 survey, 873 at least started the W2 survey. Data quality checks were employed in line with best practices for online surveys (e.g., removing respondents who did not complete most of the survey or who did not pass the attention filters). After data quality checks, 5.2% of respondents were removed from the sample, resulting in a final sample size of 828 parents (a response rate of 72%).
In the second stage, a new sample of parents was recruited. New parents had to meet the same sampling criteria as in W1 (be at least 18 years old, reside in the United States, reside with a romantic partner, and be a parent living with at least one biological child). Also similar to the W1 procedures, we oversampled men, Black individuals, individuals who did not complete college, and individuals who identified as politically conservative to increase sample diversity. A total of 1,207 parents participated in the W2 survey. Data quality checks led to the removal of 5.7% of the respondents, resulting in a final sample size of new respondents at Wave 2 of 1,138 parents.
In both stages, participants were informed that the survey would take approximately 20 minutes to complete. All panelists were provided monetary compensation in line with Prolific’s compensation guidelines, which require that all participants earn above minimum wage for their time participating in studies.
To be included in SPDLC, respondents had to meet the following sampling criteria at the time they enter the study: (a) be at least 18 years old, (b) reside in the United States, (c) reside with a romantic partner (i.e., be married or cohabiting), and (d) be a parent living with at least one biological child. Follow-up respondents must be at least 18 years old and reside in the United States, but may experience changes in relationship and resident parent statuses. Smallest Geographic Unit: U.S. StateThis work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. In accordance with this license, all users of these data must give appropriate credit to the authors in any papers, presentations, books, or other works that use the data. A suggested citation to provide attribution for these data is included below:
To help provide estimates that are more representative of U.S. partnered parents, the SPDLC includes sampling weights. Weights can be included in statistical analyses to make estimates from the SPDLC sample representative of U.S. parents who reside with a romantic partner (married or cohabiting) and a child aged 18 or younger based on age, race/ethnicity, and gender. National estimates for the age, racial/ethnic, and gender profile of U.S. partnered parents were obtained using data from the 2020 Current Population Survey (CPS). Weights were calculated using an iterative raking method, such that the full sample in each data file matches the nationally representative CPS data in regard to the gender, age, and racial/ethnic distributions within the data. This variable is labeled CPSweightW2 in the Wave 2 dataset, and CPSweightLW2 in the longitudinal dataset (which includes Waves 1 and 2). There is not a weight variable included in the W1-W2 repeated cross-section data file.
Carlson, Daniel L. and Richard J. Petts. 2022. Study on U.S. Parents’ Divisions of Labor During COVID-19 User Guide: Waves 1-2.
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