How Proper Scoring Rules Shape LLM Forecasting

This paper evaluates how reward function choice shapes the performance and behavior of LLM forecasters. We compare five proper scoring rules as training objectives for binary forecasts of resolved real-world events. Although the rules share the same theoretical incentive for truthful probability reporting, the resulting models differ in calibration, probability use, and estimated profiles of bias, information, and noise, with smaller differences in aggregate accuracy and discrimination. The Brier-trained model has the lowest observed Brier score and highest AUC-ROC, while the log-trained model has the highest observed log score and lowest calibration error. Models with similar aggregate performance also reach that performance through different combinations of bias, information, and noise. Proper scoring rules therefore need not behave interchangeably as training objectives. Reward choice may shape not only how well an LLM forecasts, but how its forecasting errors are structured. Each condition uses a single seed, so some differences may reflect training stochasticity.

A Framework for Designing Reward Functions: From Objectives to Features to Human-Aligned Reward Functions

We present a formal process to enable non-experts to instantiate and iterate on human-aligned reward functions, i.e. reward functions that adhere to a given preference ordering over trajectories. Given a task described in natural language, our process produces a linear reward function in three steps: distill the task's objectives into a set of fundamental objectives and derive measurable outcome variables that capture those fundamental objectives, select a causally representative subset of outcome variables as the reward terms, and fit weights to those reward terms via preference elicitation. Our contributions describe the first step and formalize the latter two steps. The first is a guided workflow for deriving outcome variables. The second is a reduction of reward term selection to minimum-cost partial cover on a causal DAG, solved in polynomial time via max-flow. The third is a geometric framing of weight fitting as a convex feasibility problem iteratively narrowed by preference queries, solved by existing separation oracle methods. To the best of our knowledge, this is the first reward-design method that maintains a deterministically conflict-free feasible weight region, narrowed to a desired tolerance via a separation oracle with O(n log κ) preference queries.