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Background: RETFound, a self-supervised, retina-specific foundation model (FM), showed potential in downstream applications. However, its comparative performance with traditional deep learning (DL) models remains incompletely understood. This study aimed to evaluate RETFound against three ImageNet-pretrained supervised DL models (ResNet50, ViT-base, SwinV2) in detecting ocular and systemic diseases. Methods: We fine-tuned/trained RETFound and three DL models on full datasets, 50%, 20%, and fixed sample sizes (400, 200, 100 images, with half comprising disease cases; for each DR severity class, 100 and 50 cases were used. Fine-tuned models were tested internally using the SEED (53,090 images) and APTOS-2019 (3,672 images) datasets and externally validated on population-based (BES, CIEMS, SP2, UKBB) and open-source datasets (ODIR-5k, PAPILA, GAMMA, IDRiD, MESSIDOR-2). Model performance was compared using area under the receiver operating characteristic curve (AUC) and Z-tests with Bonferroni correction (P<0.05/3). Interpretation: Traditional DL models are mostly comparable to RETFound for ocular disease detection with large datasets. However, RETFound is superior in systemic disease detection with smaller datasets. These findings offer valuable insights into the respective merits and limitation of traditional models and FMs.

Combinatorial bilevel congestion pricing (CBCP), a variant of the discrete network design problem, seeks to minimize the total travel time experienced by all travelers in a road network, by strategically selecting toll locations and determining the corresponding charges. Conventional wisdom suggests that these problems are intractable since they have to be formulated and solved with a significant number of integer variables. Here, we devise a scalable local algorithm for the CBCP problem that guarantees convergence to a Kuhn-Tucker-Karush point. Our approach is novel in that it eliminates the use of integer variables altogether, instead introducing a cardinality constraint that limits the number of toll locations to a user-specified upper bound. The resulting bilevel program with the cardinality constraint is then transformed into a block-separable, single-level optimization problem that can be solved efficiently after penalization and decomposition. We are able to apply the algorithm to solve, in about 20 minutes, a CBCP instance with up to 3,000 links, of which hundreds can be tolled. To the best of our knowledge, no existing algorithm can solve CBCP problems at such a scale while providing any assurance of convergence.

As one of the most fundamental concepts in transportation science, Wardrop equilibrium (WE) has always had a relatively weak behavioral underpinning. To strengthen this foundation, one must reckon with bounded rationality in human decision-making processes, such as the lack of accurate information, limited computing power, and sub-optimal choices. This retreat from behavioral perfectionism in the literature, however, was typically accompanied by a conceptual modification of WE. Here, we show that giving up perfect rationality need not force a departure from WE. On the contrary, WE can be reached with global stability in a routing game played by boundedly rational travelers. We achieve this result by developing a day-to-day (DTD) dynamical model that mimics how travelers gradually adjust their route valuations, hence choice probabilities, based on past experiences. Our model, called cumulative logit (CumLog), resembles the classical DTD models but makes a crucial change: whereas the classical models assume routes are valued based on the cost averaged over historical data, ours values the routes based on the cost accumulated. To describe route choice behaviors, the CumLog model only uses two parameters, one accounting for the rate at which the future route cost is discounted in the valuation relative to the past ones and the other describing the sensitivity of route choice probabilities to valuation differences. We prove tha CumLog always converges to WE, regardless of the initial point, as long as the behavioral parameters satisfy certain mild conditions. Our theory thus upholds WE's role as a benchmark in transportation systems analysis. It also resolves the theoretical challenge posed by Harsanyi's instability problem by explaining why equally good routes at WE are selected with different probabilities.

In this paper, we develop an approximation scheme for solving bilevel programs with equilibrium constraints, which are generally difficult to solve. Among other things, calculating the first-order derivative in such a problem requires differentiation across the hierarchy, which is computationally intensive, if not prohibitive. To bypass the hierarchy, we propose to bound such bilevel programs, equivalent to multiple-followers Stackelberg games, with two new hierarchy-free problems: a $T$-step Cournot game and a $T$-step monopoly model. Since they are standard equilibrium or optimization problems, both can be efficiently solved via first-order methods. Importantly, we show that the bounds provided by these problems -- the upper bound by the $T$-step Cournot game and the lower bound by the $T$-step monopoly model -- can be made arbitrarily tight by increasing the step parameter $T$ for a wide range of problems. We prove that a small $T$ usually suffices under appropriate conditions to reach an approximation acceptable for most practical purposes. Eventually, the analytical insights are highlighted through numerical examples.

In a Stackelberg congestion game (SCG), a leader aims to maximize their own gain by anticipating and manipulating the equilibrium state at which the followers settle by playing a congestion game. Often formulated as bilevel programs, large-scale SCGs are well known for their intractability and complexity. Here, we attempt to tackle this computational challenge by marrying traditional methodologies with the latest differentiable programming techniques in machine learning. The core idea centers on replacing the lower-level equilibrium problem with a smooth evolution trajectory defined by the imitative logit dynamic (ILD), which we prove converges to the equilibrium of the congestion game under mild conditions. Building upon this theoretical foundation, we propose two new local search algorithms for SCGs. The first is a gradient descent algorithm that obtains the derivatives by unrolling ILD via differentiable programming. Thanks to the smoothness of ILD, the algorithm promises both efficiency and scalability. The second algorithm adds a heuristic twist by cutting short the followers' evolution trajectory. Behaviorally, this means that, instead of anticipating the followers' best response at equilibrium, the leader seeks to approximate that response by only looking ahead a limited number of steps. Our numerical experiments are carried out over various instances of classic SCG applications, ranging from toy benchmarks to large-scale real-world examples. The results show the proposed algorithms are reliable and scalable local solvers that deliver high-quality solutions with greater regularity and significantly less computational effort compared to the many incumbents included in our study.

To regulate a social system comprised of self-interested agents, economic incentives are often required to induce a desirable outcome. This incentive design problem naturally possesses a bilevel structure, in which a designer modifies the rewards of the agents with incentives while anticipating the response of the agents, who play a non-cooperative game that converges to an equilibrium. The existing bilevel optimization algorithms raise a dilemma when applied to this problem: anticipating how incentives affect the agents at equilibrium requires solving the equilibrium problem repeatedly, which is computationally inefficient; bypassing the time-consuming step of equilibrium-finding can reduce the computational cost, but may lead the designer to a sub-optimal solution. To address such a dilemma, we propose a method that tackles the designer's and agents' problems simultaneously in a single loop. Specifically, at each iteration, both the designer and the agents only move one step. Nevertheless, we allow the designer to gradually learn the overall influence of the incentives on the agents, which guarantees optimality after convergence. The convergence rate of the proposed scheme is also established for a broad class of games., Comment: Accepted by the Thirty-sixth Conference on Neural Information Processing Systems (NeurIPS 2022)

In this paper, we attempt to estimate the effect of the implementation of subscription-based streaming services on the demand of the associated game consoles. We do this by applying the BLP demand estimation model proposed by Berry (1994). This results in a linear demand specification which can be identified using conventional identification methods such as instrumental variables estimation and fixed-effects models. We find that given our dataset, the two-stage least squares (2SLS) regression provides us with convincing estimates that subscription-based streaming services does have a positive effect on the demand of game consoles as proposed by the general principle of complementary goods.

We seek to take a different approach in deriving the optimal search policy for the repeated consumer search model found in Fishman and Rob (1995) with the main motivation of dropping the assumption of prior knowledge of the price distribution $F(p)$ in each period. We will do this by incorporating the famous multi-armed bandit problem (MAB). We start by modifying the MAB framework to fit the setting of the repeated consumer search model and formulate the objective as a dynamic optimization problem. Then, given any sequence of exploration, we assign a value to each store in that sequence using Bellman equations. We then proceed to break down the problem into individual optimal stopping problems for each period which incidentally coincides with the framework of the famous secretary problem where we proceed to derive the optimal stopping policy. We will see that implementing the optimal stopping policy in each period solves the original dynamic optimization by `forward induction' reasoning.

In 2014 the Patient Protection and Affordable Care Act (ACA) introduced the expansion of Medicaid where states can opt to expand the eligibility for those in need of free health insurance. In this paper, we attempt to assess the effectiveness of Medicaid expansion on health outcomes of state populations using Difference-in-Difference (DD) regressions to seek for causal impacts of expanding Medicaid on health outcomes in 49 states. We find that in the time frame of 2013 to 2016, Medicaid expansion seems to have had no significant impact on the health outcomes of states that have chosen to expand.

In a social system, the self-interest of agents can be detrimental to the collective good, sometimes leading to social dilemmas. To resolve such a conflict, a central designer may intervene by either redesigning the system or incentivizing the agents to change their behaviors. To be effective, the designer must anticipate how the agents react to the intervention, which is dictated by their often unknown payoff functions. Therefore, learning about the agents is a prerequisite for intervention. In this paper, we provide a unified framework for learning and intervention in games. We cast the equilibria of games as individual layers and integrate them into an end-to-end optimization framework. To enable the backward propagation through the equilibria of games, we propose two approaches, respectively based on explicit and implicit differentiation. Specifically, we cast the equilibria as the solutions to variational inequalities (VIs). The explicit approach unrolls the projection method for solving VIs, while the implicit approach exploits the sensitivity of the solutions to VIs. At the core of both approaches is the differentiation through a projection operator. Moreover, we establish the correctness of both approaches and identify the conditions under which one approach is more desirable than the other. The analytical results are validated using several real-world problems., Comment: To be published in Advances in Neural Information Processing Systems 33 (NeurIPS 2020)