Why do some students delay college enrollment? Does it matter?

Over one third of students in the U.S. who started college in 2012 did not enroll in the fall immediately following their high school graduation. Despite the prevalence of delayed college enrollment, however, little is known about the reasons for the delay and the consequences for academic and labor markets outcomes. Conventional human capital theory suggests that formal education should precede work in order to maximize the period of benefiting from the returns of investment in education. As such, the reasons for students delaying their college enrollment are still unclear. Usually, it has been perceived either as an irrational behavior, or a constrained behavior caused by the imperfect market. The first chapter of this dissertation provides an overview of the studies that explain the phenomenon of delay, and I conclude that financial constraint is not the only explanation. Students might rationally adjust the timing of enrollment to maximize their welfare, based on their personal capabilities, preferences, and economic conditions. Factors such as behavioral bias and sociological constraints also influence students’ educational decisions. Based on the theoretical framework proposed in the first chapter, it is predominantly believed that college enrollment could be countercyclical, especially for students who are financially constrained. The second chapter takes advantage of a natural experiment and discovers one of the factors that causes college enrollment delay: the housing market boom. I use the Education Longitudinal Survey: 2002 and the Building Permit Survey to estimate the effect of local housing market booms on college enrollment timing. I find that an additional 100 increase in the annual change of building permits leads to 0.24 percentage-point increase in enrollment delay for male high school graduates. However, the temporary delay in transition to college that is caused by a housing boom does not necessarily decrease the college enrollment rate eight years, but it makes returners less likely to enroll in four-year colleges. Using data from the National Longitudinal Survey of Youth 1997, the third chapter of this dissertation examines the characteristics and earnings trajectories of delayers and the effects of this choice on academic and labor market outcomes. Propensity score matching results show that delaying college enrollment decreases individuals’ likelihood of enrolling in college, and increases their tendency to enroll in two-year colleges if they return to school. The results also demonstrate that, consistent with the study’s descriptive results, the early earnings benefits that are experienced by delayers diminish after their mid-20s and turn to significant losses over time. Oaxaca decomposition results indicate that differences in student characteristics only explain one third of the pay gap between the two groups; 60% of the pay gap is explained by delayers’ reduced likelihood of attending and obtaining a degree at a four-year college

Backward Imitation and Forward Reinforcement Learning via Bi-directional Model Rollouts

Traditional model-based reinforcement learning (RL) methods generate forward rollout traces using the learnt dynamics model to reduce interactions with the real environment. The recent model-based RL method considers the way to learn a backward model that specifies the conditional probability of the previous state given the previous action and the current state to additionally generate backward rollout trajectories. However, in this type of model-based method, the samples derived from backward rollouts and those from forward rollouts are simply aggregated together to optimize the policy via the model-free RL algorithm, which may decrease both the sample efficiency and the convergence rate. This is because such an approach ignores the fact that backward rollout traces are often generated starting from some high-value states and are certainly more instructive for the agent to improve the behavior. In this paper, we propose the backward imitation and forward reinforcement learning (BIFRL) framework where the agent treats backward rollout traces as expert demonstrations for the imitation of excellent behaviors, and then collects forward rollout transitions for policy reinforcement. Consequently, BIFRL empowers the agent to both reach to and explore from high-value states in a more efficient manner, and further reduces the real interactions, making it potentially more suitable for real-robot learning. Moreover, a value-regularized generative adversarial network is introduced to augment the valuable states which are infrequently received by the agent. Theoretically, we provide the condition where BIFRL is superior to the baseline methods. Experimentally, we demonstrate that BIFRL acquires the better sample efficiency and produces the competitive asymptotic performance on various MuJoCo locomotion tasks compared against state-of-the-art model-based methods.Comment: Accepted by IROS202

On a conjecture of Ghorpade, Datta and Beelen for the number of points of varities over finite fields

Consider a finite field $\mathbb{F}_q$ and positive integers $d,m,r$ with $1\leq r\leq \binom{m+d}{d}$. Let $S_d(m)$ be the $\mathbb{F}_q$ vector space of all homogeneous polynomials of degree $d$ in $X_0,\dots,X_m$. Let $e_r(d,m)$ be the maximum number of $\mathbb{F}_q$-rational points in the vanishing set of $W$ as $W$ varies through all subspaces of $S_d(m)$ of dimension $r$. Ghorpade, Datta and Beelen had conjectured an exact formula of $e_r(d,m)$ when $q\geq d+1$. We prove that their conjectured formula is true when $q$ is sufficiently large in terms of $m,d,r$. The problem of determining $e_r(d,m)$ is equivalent to the problem of computing the $r^{th}$ generalized hamming weights of projective the Reed Muller code $PRM_q(d,m)$. It is also equivalent to the problem of determining the maximum number of points on sections of Veronese varieties by linear subvarieties of codimension $r$