Mass public quarantining, colloquially known as a lock-down, is a non-pharmaceutical intervention to check spread of disease. This paper presents ESOP (Epidemiologically and Socioeconomically Optimal Policies), a novel application of active machine learning techniques using Bayesian optimization, that interacts with an epidemiological model to arrive at lock-down schedules that optimally balance public health benefits and socioeconomic downsides of reduced economic activity during lock-down periods. The utility of ESOP is demonstrated using case studies with VIPER (Virus-Individual-Policy-EnviRonment), a stochastic agent-based simulator that this paper also proposes. However, ESOP is flexible enough to interact with arbitrary epidemiological simulators in a black-box manner, and produce schedules that involve multiple phases of lock-downs. Keywords Optimal policy • Lock-down • Epidemiology • Bayesian optimization Disclaimer This paper makes no recommendation to individuals and its results should not be interpreted by individuals to modulate personal behavior. The authors recommend that individuals continue to follow guidelines offered by local governments with respect to lock-downs and social distancing, and those offered by medical professionals with respect to personal hygiene and treatment.

Mass public quarantining, colloquially known as a lock-down, is a non-pharmaceutical intervention to check spread of disease. This paper presents ESOP (Epidemiologically and Socio-economically Optimal Policies) 1 , a novel application of active machine learning techniques using Bayesian optimization, that interacts with an epidemiological model to arrive at lock-down schedules that optimally balance public health benefits and socio-economic downsides of reduced economic activity during lock-down periods. The utility of ESOP is demonstrated using case studies with VIPER (Virus-Individual-Policy-EnviRonment), a stochastic agent-based simulator that this paper also proposes. However, ESOP is flexible enough to interact with arbitrary epidemiological simulators in a black-box manner, and produce schedules that involve multiple phases of lock-downs. Disclaimer: This paper makes no recommendation to individuals and its results should not be interpreted by individuals to modulate personal behavior. The authors recommend that individuals continue to follow guidelines offered by local governments with respect to lock-downs and social distancing, and those offered by medical professionals with respect to personal hygiene and treatment.

One often needs to turn a coupling (X i , Y i ) i≥0 of a Markov chain into a sticky coupling where once X T = Y T at some T , then from then on, at each subsequent time step T ′ ≥ T , we shall have X T ′ = Y T ′ . However, not all of what are considered couplings in literature, even Markovian couplings, can be turned into sticky couplings, as proved by Rosenthal [Ro97] through a counter example. Rosenthal then proposed a strengthening of the Markovian coupling notion, termed as faithful coupling, from which a sticky coupling can indeed be obtained. We identify the reason why a sticky coupling could not be obtained in the counter example of Rosenthal, which motivates us to define a type of coupling which can obviously be turned into a sticky coupling. We show then that the new type of coupling that we define, and the faithful coupling as defined by Rosenthal [Ro97], are actually identical. Our note may be seen as a demonstration of the naturalness of the notion of faithful coupling.

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This paper presents SVAM (Sequential Variance-Altered MLE), a unified framework for learning generalized linear models under adversarial label corruption in training data. SVAM extends to tasks such as least squares regression, logistic regression, and gamma regression, whereas many existing works on learning with label corruptions focus only on least squares regression. SVAM is based on a novel variance reduction technique that may be of independent interest and works by iteratively solving weighted MLEs over variance-altered versions of the GLM objective. SVAM offers provable model recovery guarantees superior to the state-of-the-art for robust regression even when a constant fraction of training labels are adversarially corrupted. SVAM also empirically outperforms several existing problem-specific techniques for robust regression and classification. Code for SVAM is available at https://github.com/purushottamkar/svam/