Taylor Lundy

Chris Cameron, Jason Hartford, Taylor Lundy et al.

We introduce Monte Carlo Forest Search (MCFS), a class of reinforcement learning (RL) algorithms for learning policies in {tree MDPs}, for which policy execution involves traversing an exponential-sized tree. Examples of such problems include proving unsatisfiability of a SAT formula; counting the number of solutions of a satisfiable SAT formula; and finding the optimal solution to a mixed-integer program. MCFS algorithms can be seen as extensions of Monte Carlo Tree Search (MCTS) to cases where, rather than finding a good path (solution) within a tree, the problem is to find a small tree within a forest of candidate trees. We instantiate and evaluate our ideas in an algorithm that we dub Knuth Synthesis, an MCFS algorithm that learns DPLL branching policies for solving the Boolean satisfiability (SAT) problem, with the objective of achieving good average-case performance on a given distribution of unsatisfiable problem instances. Knuth Synthesis is the first RL approach to avoid the prohibitive costs of policy evaluations in an exponentially-sized tree, leveraging two key ideas: first, we estimate tree size by randomly sampling paths and measuring their lengths, drawing on an unbiased approximation due to Knuth (1975); second, we query a strong solver at a user-defined depth rather than learning a policy across the whole tree, to focus our policy search on early decisions that offer the greatest potential for reducing tree size. We matched or exceeded the performance of a strong baseline on three well-known SAT distributions, facing problems that were two orders of magnitude more challenging than those addressed in previous RL studies.

Taylor Lundy, Narun K. Raman, Kevin Leyton-Brown

LLM benchmarks are increasingly dynamic: instead of containing a fixed set of questions, they define templates and parameters that can generate an effectively unlimited number of question variants. This flexibility is valuable, but it makes evaluation expensive -- especially when the goal is not just determining an average score, but reliably identifying a model's weak spots. This paper introduces a new methodology for identifying hard questions in dynamic benchmarks. It leverages COUP, a recent Bayesian optimization algorithm (Graham, Velez & Leyton-Brown, 2026), after introducing several substantive modifications to make the algorithm suitable for practical LLM pipelines. We also wrap it in a tool that supports flexible choices of datasets and utility functions, enabling users to target the kinds of questions they care about (e.g., low-accuracy questions; questions that are unusually hard relative to their measured complexity). In experiments across a range of benchmarks, we show that our method, dubbed $\texttt{QuickScope}$, discovers truly difficult questions more sample efficiently than standard baselines, while also reducing false positives from noisy outcomes.

Narun Raman, Taylor Lundy, Thiago Amin et al.

How should one judge whether a given large language model (LLM) can reliably perform economic reasoning? Most existing LLM benchmarks focus on specific applications and fail to present the model with a rich variety of economic tasks. A notable exception is Raman et al. [2024], who offer an approach for comprehensively benchmarking strategic decision-making; however, this approach fails to address the non-strategic settings prevalent in microeconomics, such as supply-and-demand analysis. We address this gap by taxonomizing microeconomic reasoning into $58$ distinct elements, focusing on the logic of supply and demand, each grounded in up to $10$ distinct domains, $5$ perspectives, and $3$ types. The generation of benchmark data across this combinatorial space is powered by a novel LLM-assisted data generation protocol that we dub auto-STEER, which generates a set of questions by adapting handwritten templates to target new domains and perspectives. Because it offers an automated way of generating fresh questions, auto-STEER mitigates the risk that LLMs will be trained to over-fit evaluation benchmarks; we thus hope that it will serve as a useful tool both for evaluating and fine-tuning models for years to come. We demonstrate the usefulness of our benchmark via a case study on $27$ LLMs, ranging from small open-source models to the current state of the art. We examined each model's ability to solve microeconomic problems across our whole taxonomy and present the results across a range of prompting strategies and scoring metrics.

Narun Raman, Taylor Lundy, Samuel Amouyal et al.

There is increasing interest in using LLMs as decision-making "agents." Doing so includes many degrees of freedom: which model should be used; how should it be prompted; should it be asked to introspect, conduct chain-of-thought reasoning, etc? Settling these questions -- and more broadly, determining whether an LLM agent is reliable enough to be trusted -- requires a methodology for assessing such an agent's economic rationality. In this paper, we provide one. We begin by surveying the economic literature on rational decision making, taxonomizing a large set of fine-grained "elements" that an agent should exhibit, along with dependencies between them. We then propose a benchmark distribution that quantitatively scores an LLMs performance on these elements and, combined with a user-provided rubric, produces a "STEER report card." Finally, we describe the results of a large-scale empirical experiment with 14 different LLMs, characterizing the both current state of the art and the impact of different model sizes on models' ability to exhibit rational behavior.

Narun Raman, Taylor Lundy, Kevin Leyton-Brown

When evaluating Large Language Models (LLMs) in question answering domains, it is common to ask the model to choose among a fixed set of choices (so-called multiple-choice question-answering, or MCQA). Although downstream tasks of interest typically do not provide systems with explicit options among which to choose, this approach is nevertheless widely used because it makes automatic grading straightforward and has tended to produce challenging benchmarks that correlate sufficiently well with downstream performance. This paper investigates the extent to which this trend continues to hold for state-of-the-art reasoning models, describing a systematic evaluation of 15 different question-answering benchmarks (e.g., MMLU, GSM8K) and 27 different LLMs (including small models such as Qwen-2.5 7B, mid-sized models such as Llama-3.3 70B, and large state-of-the-art models such as OpenAI's o3). For each model--benchmark pair, we considered 5 ways of presenting the model with questions, including variations on whether multiple choices were offered to the model at all; whether "none of the above" sometimes replaced the right answer; and whether the model was permitted to perform chain-of-thought reasoning before and/or after the choices were presented. MCQA remained a good proxy for the downstream performance of models as long as they were allowed to perform chain-of-thought reasoning only \emph{before} being presented with the options among which they had to select. On the other hand, large models that were able to perform reasoning \emph{after} being given a set of options tended to significantly outperform their free-text performance due to exploiting the information in the options. We identify and quantify the signals models are using when answering MCQA questions, and offer practical guidelines when analyzing results from MCQA that better reflect LLMs' genuine reasoning capabilities.

Chris Cameron, Jason Hartford, Taylor Lundy et al.

Formulating real-world optimization problems often begins with making predictions from historical data (e.g., an optimizer that aims to recommend fast routes relies upon travel-time predictions). Typically, learning the prediction model used to generate the optimization problem and solving that problem are performed in two separate stages. Recent work has showed how such prediction models can be learned end-to-end by differentiating through the optimization task. Such methods often yield empirical improvements, which are typically attributed to end-to-end making better error tradeoffs than the standard loss function used in a two-stage solution. We refine this explanation and more precisely characterize when end-to-end can improve performance. When prediction targets are stochastic, a two-stage solution must make an a priori choice about which statistics of the target distribution to model-we consider expectations over prediction targets-while an end-to-end solution can make this choice adaptively. We show that the performance gap between a two-stage and end-to-end approach is closely related to the price of correlation concept in stochastic optimization and show the implications of some existing POC results for the predict-then-optimize problem. We then consider a novel and particularly practical setting, where multiple prediction targets are combined to obtain each of the objective function's coefficients. We give explicit constructions where (1) two-stage performs unboundedly worse than end-to-end; and (2) two-stage is optimal. We use simulations to experimentally quantify performance gaps and identify a wide range of real-world applications from the literature whose objective functions rely on multiple prediction targets, suggesting that end-to-end learning could yield significant improvements.

Devon Graham, Satish Kumar Sarraf, Taylor Lundy et al.

On-street parking is convenient, but has many disadvantages: on-street spots come at the expense of other road uses such as traffic lanes, transit lanes, bike lanes, or parklets; drivers looking for parking contribute substantially to traffic congestion and hence to greenhouse gas emissions; safety is reduced both due to the fact that drivers looking for spots are more distracted than other road users and that people exiting parked cars pose a risk to cyclists. These social costs may not be worth paying when off-street parking lots are nearby and have surplus capacity. To see where this might be true in downtown Vancouver, we used artificial intelligence techniques to estimate the amount of time it would take drivers to both park on and off street for destinations throughout the city. For on-street parking, we developed (1) a deep-learning model of block-by-block parking availability based on data from parking meters and audits and (2) a computational simulation of drivers searching for an on-street spot. For off-street parking, we developed a computational simulation of the time it would take drivers drive from their original destination to the nearest city-owned off-street lot and then to queue for a spot based on traffic and lot occupancy data. Finally, in both cases we also computed the time it would take the driver to walk from their parking spot to their original destination. We compared these time estimates for destinations in each block of Vancouver's downtown core and each hour of the day. We found many areas where off street would actually save drivers time over searching the streets for a spot, and many more where the time cost for parking off street was small. The identification of such areas provides an opportunity for the city to repurpose valuable curbside space for community-friendly uses more in line with its transportation goals.