Pandemics involve the high transmission of a disease that impacts global and
local health and economic patterns. The impact of a pandemic can be minimized
by enforcing certain restrictions on a community. However, while minimizing
infection and death rates, these restrictions can also lead to economic crises.
Epidemiological models help propose pandemic control strategies based on
non-pharmaceutical interventions such as social distancing, curfews, and
lockdowns, reducing the economic impact of these restrictions. However,
designing manual control strategies while considering disease spread and
economic status is non-trivial. Optimal strategies can be designed through
multi-objective reinforcement learning (MORL) models, which demonstrate how
restrictions can be used to optimize the outcome of a pandemic. In this
research, we utilized an epidemiological Susceptible, Exposed, Infected,
Recovered, Deceased (SEIRD) model: a compartmental model for virtually
simulating a pandemic day by day. We combined the SEIRD model with a deep
double recurrent Q-network to train a reinforcement learning agent to enforce
the optimal restriction on the SEIRD simulation based on a reward function. We
tested two agents with unique reward functions and pandemic goals to obtain two
strategies. The first agent placed long lockdowns to reduce the initial spread
of the disease, followed by cyclical and shorter lockdowns to mitigate the
resurgence of the disease. The second agent provided similar infection rates
but an improved economy by implementing a 10-day lockdown and 20-day
no-restriction cycle. This use of reinforcement learning and epidemiological
modeling allowed for both economic and infection mitigation in multiple
pandemic scenarios.

通过使用多目标强化学习和流行病学模型，研究提供了一种优化决策的方法来同时减少经济影响和感染率的多种大流行病场景。

通过强化学习对流行病控制政策的建模与优化

Modeling and Optimization of Epidemiological Control Policies Through  Reinforcement Learning

Many scenarios where agents with restrictions compete for resources can be
cast as maximum matching problems on bipartite graphs. Our focus is on resource
allocation problems where agents may have restrictions that make them
incompatible with some resources. We assume that a Principle chooses a maximum
matching randomly so that each agent is matched to a resource with some
probability. Agents would like to improve their chances of being matched by
modifying their restrictions within certain limits. The Principle's goal is to
advise an unsatisfied agent to relax its restrictions so that the total cost of
relaxation is within a budget (chosen by the agent) and the increase in the
probability of being assigned a resource is maximized. We establish hardness
results for some variants of this budget-constrained maximization problem and
present algorithmic results for other variants. We experimentally evaluate our
methods on synthetic datasets as well as on two novel real-world datasets: a
vacation activities dataset and a classrooms dataset.

本文研究了有资源分配约束限制的多智能体竞争问题，提出了基于最大匹配问题的解决方案，围绕基于预算限制下最大化匹配效果的约束条件进行了算法研究并在两个真实数据集上进行了实验评估。

具有约束的智能体资源分配：最大化可能性，最小化妥协

Resource Allocation to Agents with Restrictions: Maximizing Likelihood with Minimum Compromise

Let $L^{m,p}(\R^n)$ be the Sobolev space of functions with $m^{th}$
derivatives lying in $L^p(\R^n)$. Assume that $n< p < \infty$. For $E \subset
\R^n$, let $L^{m,p}(E)$ denote the space of restrictions to $E$ of functions in
$L^{m,p}(\R^n)$. We show that there exists a bounded linear map $T : L^{m,p}(E)
\rightarrow L^{m,p}(\R^n)$ such that, for any $f \in L^{m,p}(E)$, we have $Tf =
f$ on $E$. We also give a formula for the order of magnitude of
$\|f\|_{L^{m,p}(E)}$ for a given $f : E \rightarrow \R$ when $E$ is finite.

研究 Sobolev 空间的函数限制与其在整个空间上的函数之间存在有界线性映射的关系，并给出了限制集合为有限集合时，函数在该集合上范数的数量级计算公式。