Outcome-based Reinforcement Learning to Predict the Future
Authors: Benjamin Turtel
Danny Franklin
Kris Skotheim
Luke Hewitt
Philipp Schoenegger
Venue: Accepted by TMLR ()

Abstract: Reinforcement Learning with Verifiable Rewards (RLVR) has been an effective approach for improving Large Language Models' reasoning in domains such as coding and mathematics. Here, we apply RLVR methods towards forecasting future real-world events – a challenging task for RL due to the very noisy (and delayed) outcomes involved. Using a novel dataset of recent questions from a prediction market, and accompanying relevant news headlines, we show that a compact (14B) reasoning model can be trained to match or surpass the predictive accuracy of frontier models like o1, while greatly improving probabilistic calibration. The model's performance is also practically meaningful: in a Polymarket trading simulation, we estimate that its bets would have yielded a return on investment of over 10\% across all questions in the test set. We detail and compare approaches used in training our model, including augmenting our training-data with synthetic prediction questions, guardrails for learning stability, and median prediction sampling at inference-time.

Published in Transactions on Machine Learning Research (11/2025)
Outcome-based Reinforcement Learning to Predict the Future
Benjamin Turtel, Danny Franklin, Kris Skotheim Lightning Rod Labs
ben@lightningrod.c ai
Luke Hewitt Stanford University
lbh @stanford. edu
Philipp Schoenegger London School of Economics and Political Science
Reviewed on OpenReview; https: // oppprevvee.........mmmm net/ per/formm? id= bbkdeL8EUX
Abstract
Reinforcement Learning with Verifiable Rewards (RIVR) has been an effective approach for improving Large Language Models' reasoning in domains such as coding and mathematics. Here, we apply RLVR methods towards forecasting future real-world events a challenging task for RL due to the very noisy (and delayed) outcomes involved. Using novel dataset of recent questions from prediction market, and accompanying relevant news headlines, we show that compact (14B) reasoning model can be trained to match surpass the predictive accuracy of frontier models like o1, while greatly improving probabilistic calibration. The model's performance also practically mcaningful: in a Polymarket trading simulation, we estimate that its bets would have yielded a relurn on investment of over 10% across all questions in the test set. We detail and compare approaches used in training our model, including augmenting our training-data with synthetic prediction questions, guardrails for learning stability, and median prediction sampling at inference-time
1 Introduction
Reinforcement learning with verifiable rewards (RLVR) has recently boosted large language model (LLM)
performance on benchmarks such as GSMSK, ATME, and MATH (Zhao et al. 2025a Shao et. al. 2024
Guo et al. 2025 Lambert et al. 2024 Xie et al. 2025). RLVR fine-tunes a base model with on-policy
reinforcement learning (RL) against objective pass/ fail signals, like unit tests or exact numeric solutions LLu et al.
2023 Su et al. 2025). Complementary self-learning work shows that mixing verifiable non-math corpora into RL. pipelines can extend these gains beyond purely symbolic tasks (Akter et al. 2025).
RLVR methods are principally applied to problems whose outcomes are deterministie and instantly verifiable (Murphy 2025). However, in this work we aim to apply RLVR methods to the problem of forecasting world events. This presents a substantial challenge, due to the inherently noisy and delayed outcomes involved: forecasting requires causal inference, trend extrapolation, and well-calibrated probabilities while supplying only sparse, lagged supervision (Weng] 2024 Qu et al. 2025). Under these conditions, we find that standard GRPPO-syle updates can drive policies toward extreme overconfidennce, gibberish output, or outright training collapso. Adapting RLVR to this setting promises to extend model reasoning ability to an especially demanding domain, palentially unlocking host of real-world applications.
In this work, we design and empirically validate stable RL pipeline for probabilistic forecasting, On the algorithmic side, we (i) remove per-question standard-deviation scaling from Group Relative Policy Optimisation (GRPO), (ii) switch to baseline-subtracted advantages in REMAX (Li et al. 2023). and (iii) add lightweight guard-rails, token-length limits, a gibberish filter, and an early-stop criterion, to keep gradients proportional to Brier loss and prevent collapse over more than 100,000 sequential events. On the evaluation
Dataset available at: http:///gggggggocccoo/////s///aa www.oodoooaaaootttooeeooeeeeee tattt---eett-tttt---taeeeett

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Published in Transactions on Machine Learning Research (11/2025)
side, we collect novel dataset of 1,265 questions on Polymarket, with accompanying news headlines up to given prediction date, taking several measures to avoid temporal leakage (a common issue when backtesting the accuracy of forecasting models, see Section 2.1.. We assess accuracy with the soft-Brier score and calibration with expected calibration error (ECE). Finally, we quantify economic value by converting cach lorecast into a set of hypothetical trades and comparing realised profits with those of the frontier reasoning model o1 as a benchmark.
Overall, we find that the 1,266-question hold-out set, seven-rum REMAX ensemble attains a Brier of 0.190 [0.178, 0.203] and an ECE of 0.062, meaning it matches surpasses o1 in accuracy while markedly improving calibration. In simulated trading scenario, in which the model places a one-share hypothetical bet on every Polymarket question in the test set, REMAX earns a profit of $52 versus S39 for o1. Thus, we find that our REMAX ENSEMBLE is able to outperform frontier reasoning models in both accuracy and calibration when forecasting future world events, and can leverage this capability to carn meaningful profit in real-money prediction markets.
2 Method
2.1
Data and Preprocessing
We begin by collecting an ordered training dataset of 10,000 training questions from Polymarket (yes/mn / contracts), including creation date, close date, resolution timestamp and final outcome. For each question we draw single prediction date uniformly at random between its on-chain open and scheduled close. For each question, we use the Exa.ai API to retrieve news headlines from before the sampled prediction date (Exa.ai offers day-level gramularity) to include in a model's prompt. This aims to ensure that the model never sees information its prompt dated on or after its own forecast.
When developing and evaluating forecasting models, it is critical to avoid sources of 'lemporal leakage', in which the model is able to use knowledge of future events implicit in its training data or prompt in order to gain an unfair advantage (Palcka et al. 2025). To construct the test sct, we follow the same approach as above, but take variely of additional steps to minimise the possibility of temporal leakage:
We construct the test set such that all questions' prediction-dates occur after the latest resolution date of any training question.
2. Many questions have indeterminate resolution dates (e.g. "Will X happen some time before Y?"), which could reveal information about the future due to selecting on ouly resolved questions. To address this, we restrict test-set questions those which were originally scheduled close by the time of dataset construction.
3. The Exa.ai API could potentially include errors in the date a given news article was published, allowing future information to leak into the prompt. To address this, we OpenAl o3 to flag any questions for which the news stories contain relevant information that should not have been known at the prediction date, and exclude these questions from the test set.
In addition, all questions with zero trading volume were excluded from the test set, in order to allow fair comparison with Polymarket forecaster predictions.
Finally, for a second set of experiments, we generate 100,000 additional training questions and answers using Lightning Rod Labs' proprietary Foresight Learning" framework. These questions follow a similar format but are created automatically without humans in the loop or labeled data. Foresight Learning creates training instances from streams of data (e.g. news articles) by using large language model to generate questions that are difficult to predict at one point in time but easier to verify at a later point in time. In the second set of experiments, we use the same 10,000 questions as the initial experiment plus an additional 100,000 generated questions mixed in and time-ordered. We reserved the same held-out test set of 1,265 questions for all models.
Examples of questions included in this test dataset are "Will Apple launch an iPhone SE on February 19?", "Will the highest temperature in London be between 37-98-F on February 16?", and " "Will Southamplon win
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2025-02-252* The full dataset (including questions, relevant news headlines to aid prediction, model reasoning traces and predictions, and the true final resolution) is available here!
2.2 Model
14- 14-billion--ee Dallionn-prrmeeter model initialised from the open-weight Qwen 2. 2-5-14B base checkpoint (Yang et al. 2024 and further instruction-tuned on the 800k-sample DeepSeek-RI distilled reasoning corpus (Zhao et al. 2025b). Our fine-tuning regimes take this as the base model and our analyses compare to this base model as well as other benchmarks and frontier models.
All experiments are conducted with DeppseeakKR--Distti-----e--
2.3 Reward Design
We treat the forecasting task as a sequential decision problem in which the model receives a textual prompt about a future event, outputs a single probability [0, 1] that the event will occur, and subsequently observes the binary outcome y E {0. The episode reward the (negative) Brier score (Brier 1950)
R = - (
-
(p-
y)² -
strictly proper scoring rule that incentivises calibrated probabilistic forecasts.
Model outputs occasionally fail to parse a valid probability, for example when the generation omits nuneric answer or when the model fails to answer altogether. During training, use the following scheme:
Strict Brier: assign the maximum Brier loss of 1.0 (equivalently training reward R= -1) whenever the regex fails to extract a probability in [0, I].
For evaluation, we use the following metric that does not penalise misformatting and missing predictions much:
Soft Brier: assign constant Brier loss of 0.25 (training reward R 0.255) to any malformed missing forecast, preserving gradient signal while avoiding training collapse.
2.3.1 RL Algorithms and Updates
We evaluate three on-policy RL algorithms, GRPO, Modified-GRPO and ReMax, and include Direct Preference Optimisation (DPO) as an off-policy baseline.
GRPO First, we test Group Relative Policy Optimization (GRPO) (Shao al. 2024). For each question
q we draw outputs (o o} from the old policy Teat (=1 and assign each output of scalar reward
r'. Let
C
G
1
A' 4
σ
rr - 222
G
G
σ
i=1
The policy is updated by maximising
1o'
JaRPO = EE,
min( cliprii, +))Aa) - (xo(Fo)t
G
10
where
To(o; q, 0.0
No (o) q, o'22)²
the clipping threshold, Ree is the reference policy reset the current policy at the start of each outer iteration, and 3 is the KL-penalty coefficient. Normalising by stabiliscs the updates, but can dampen the learning signal when particularly large rewards are important.
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Modified GRPO Second, we modify the standard GRPO algorithm by removing the standard-deviation division and set A = μ.. This preserves the raw magnitude of especially large forecast errors, potentially improving the model's ability to correct extreme miscalibrations. Yet, omitting the normalisation can make optimisation more sensitive to outliers, requiring additional guard-rails to mitigate instability 2 This modification parallels the Dr. GRPO method proposed by Liu et al. (Liu al., 2025).
ReMax Third, we also apply ReMax (Li et al. 2023) by first sampling G outputs , oO} from the old policy To (- 2), each with reward r". Let 6' be a learned baseline for each o². We set the advantage to A -r - -b, removing the need to divide by a standard deviation. The policy then updated by maximising
lo'l
TReMax (0) = go
=0)
A
Σ
log To(o) I q, (2,) - DRL (Tllfelltee))
(at)
where 3 balances a KL penalty term. Subtracting a baseline in lieu of variance normalisation often better preserves large reward signals.
DPO Lastly, also test Direct Preference Optimization Rafailov et al 2023 direct preference-basod approach. This method has shown strong performance on QA lasks as well as lorecasting lasks (Turtel el al. 2025 and functions as bascline for some of our analyses.
General Remarks and Details In our forecasting context, normalising each question's rewards by their standard deviation (as in standard GRPO) can excessively dampen large errors and encourage overconfidence: per-question normalisation flattens the reward distribution and erases the natural asymmetry whereby modest gains accrue from correct but overconfident predictions, while rare mis-predictions incur disproportionately large penaltics, the very signal the model needs to learn proper calibration. By removing per-question normalisation (Modified GRPO) or using ReMax's baseline-based approach, we beller preserves the impact of large deviations, improving calibration when probabilistic forecasts deviate significantly from eventual outcomes.
x 10-8, no weight decay), bfloat16 precision, global grad-norm clip 1.0, and an entropy bonus coefficient of 0.001. We modify only the levers cach method cares about. GRPO uses an actor learning rate of x 10-6, an initial KL penalty of 0.005, PPO ratio-clip < 0.20, and G = 4 roll-outs per prompt; Modified-GRPO is identical except that drops the division the advantage to isolate the effect of normalisation. ReMax doubles the actor learning rate to 10-6, keeps the KL schedule unchanged, and trains its learned value baseline with 1 x 10-6 under an MSE loss scaled by 0.5. DPO is run for epochs at 3 0.1 with constant x 10-5 learning rate and batch size of 128 sequences. All runs employ automatic mixed precision and gradient accumulation to emulate two sequences per GPU.
Across algorithms we keep the optimisation scaffold identical: Adamn (3) 0.9, 32 = 0.999,
All experiments ran on a single 8-GPU node. The GRPO (10k), REMAX, Modified-GRPO, DPO, and the large-scale GRPO-100k run used eight NVIDIA H100 GPUs, for approximately three days. This computational requirement is a substantial constraint for individuals, but is nonetheless a realistic resource available for many computational researchers al academic institutions.
2.4 Training Protocol and Stability Measures
Online, single-pass training All on-policy algorithms (GRPO, Modified-GRPO, REMAX) are trained strictly online: each question is encountered only once in chronological order, and its outcome is revealed immediately after the event date. We do not perform multiple epochs, as re-exposing the model to past questions after outcomes are known leads to severe over-fitting (the model essentially "learns the future" on subsequent epochs).
2This vulncrability is partly mitigated in setting because Brier are intrinsically bounded in 1), which caps the variance of individual rewards and makes the absence per-question normalisation far less destabilising than it would be for tasks with unbounded numeric losses.
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Guard-rails and failure modes Scaling the training to 100k questions introduces stability challenges, particularly related to overconfidence, where some models drift toward 0% or 100% forecasts when per-question reward normalisation is used, and the generation of invalid tezt or gibberish, where large, noisy datasets can push the policy to produce nonsensical or non-English text. This happens especially when reward gradients lail to distinguish valid forecasts from invalid ones. To maintain stable training at scale, we use a scorer that deducts reward whenever a response violates any of three checks: it flags out-of-context non-English passages, nonsense or random character strings, and the absence of an explanation for the final answer inside <think> contains tettaiinsggibbristt and explains answer and records the continnous estimates non hon_englssh__.. _ewgeish_prrporttion gibberish proportion, and explanation_ _quality (each in [0, 1J). The downstream reward subtracts penalties such as Atang x non english proportion and >gih x gibberish proportion, applies a fixed penalty Amiss when explains_ answer is false, and can add up to Aexp X explanation g when a rationale is present. The routine also hard-truncates any input beyond 16 000 characters to keep evaluation stable, and its Pydantic schema validation guarantees that any formatting error or missing key zeroes the reward.
(hhinkk...<thhinkk </think> block. During evaluation the scorer sets the Boolean fields contains contanss_oo___a _____oo_____e mon_enggish,
Baselines While our primary focus is on comparing the four RL algorithms, we also benchmark forecasts against two additional references:
1. OpenAl's o1, prompted with the same question text, to assess performance against a frontier reasoning model.
2. Market prices (Polymarket), the market's implicit probability at the time cach question was asked. For every lest question, the Polymarket price is sampled at precisely the same timestamp used for the prompt cut-off, yielding a strictly contemporaneous benchmark.
These baselines indicate how our RL-trained models perform relative to both a ofate-of-the-art commercial LLM and a real-world prediction market.
2.5 Failure Modes
We observed a set of different failure modes. For example, in the model trained with GRPO without any guardrails, we find that the model somctimes assigns a probability of to outcomes that are not impossible but rather unlikely. Assigning a probability of not something a capable forecaster would do and should be avoided by forecasting models. For example, in response to the question "Will Trump say "Ukraine" 20+ times during Macron presser today?", the model outputs
[..]] In conclusion, while Ukraine will definitely be topic, the number of mentions reaching 20 is astronomically low. Even if every statement and answer included "Ukraine," it's improbable to reach that mumber. Therefore, my estimate is that the probability is extremely low, almost zero. </think> $0.000
Similarly, the model shows this overconfidence also on the other end of the probability spectrum. While acknowledging that it may have misunderstood something, it assigns probability of to questions that the model itself is somewhat unsure about: "Therefore, unless I'm missing something, the probability is 1." Overall, this model has 39.3% of predictions in either the 0- 10% or the 90-100% bucket, with many landing exactly on and 1, which shows a prevalence for very high or low probabilities.
Using our Modified GRPO approach, again without any guardrails, we do find that the model is more likely to avoid the extreme overconfidence of the standard GRPO approach, with only a total of 7.9% of predictions landing in either of the extreme buckets. However, we do observe different failure mode. Some of the answers show language switching between Chinese and English within an oulput, "Alright, so need to Patrick Mahomes ( Si LXIX T UtNl # &8, A gibberish, such as "Next, I look at the ... think that would happen in this interview," "I s...," " "Lamar Jac... that," " and "They talk about the theme, ticket distribution, and guests, but t.. that they're involved."
2 rush 30+, 3 "Over", z "Under". H # μ fut while others show partial segments of ungrammatical phrases and
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When training the model with our set of guardrails in place the 100k data set, both types of failure modes are less pronounced. For example, 13.1% 1% of predictions fell into the 0-10% and 90-100% buckets, with many forecasts that were close to 0% now having values that are greater than 0. Similarly, gibberish responses are less likely, though some ungrammatical phrases and clisions remain, such as in "Looking a. .ulld impact the price."
Brier score
Expected calibration error
OpenAl o1
0,202
0.093
Base model
(Deepseek-R1 14B)
0.215
0.089
GRPO, No guardrails
Training algorithm
0.215
0.131
Train set: Polymarket-100 10k
DPO
0.204
0:129
Mod GRPO, No guardrails
0.204
0.107
Remax, No guardrails
0.199
0.067
Train set: Lightning- 100k
Mod GRPO
0,192
0.054
Remax
0.191
0.050
Remax, Ensemble-7
0.190
0.062
0.18
0.19
0.20
0.21
0.22
0.23
0.04
0.08
0.12
0.16
Figure Mean soft-Brier score (accuracy, left) and mean expected calibration error (ECE, right) for each training algorithm the Polymarket hold-out set. Error bars show 95% confidence intervals. Lower values are better on both axes.
3 Results
3.1
Training Algorithm Comparisons
We measure predictive accuracy with the soft-Brier score, defined as the squared error (p y)² averaged over all 1,265 questions but assigning soft penalty of 0.25 whenever model fails to produce parseable probability. A score of 0.25 is equivalent to guessing 50% on a question, and thus functions a suitable stand-in for failed responses. For calibration, we use the expected calibration error (ECE) computed in ten equal-mass probability bins. For both accuracy and calibration, lower scores indicate higher accuracy and better calibration respectively. All statistics are paired across the identical question set; confidence intervals (CT) are two-sided 95% Wald intervals for Brier and bootstrap intervals for ECE unless specified herwiise every valuu reported below two-sided.
As shown in Figure I among the 10k-trained models, the model optimized using ReMax most accurate, with a soft-Brier score of 0.199 [0.187, 0.211]. This model also achieved the best probabilistic calibration, with an expected calibration error of 0.067 [0.047, 0.087J. In our follow-up experiment scaling ReMax to the 100k Lightning corpus, and ensembling the predictions across samples, achieved a Brier score of 0.190 [0.178, 0.203] and an ECE of 0.062 [0.041,0.082].
Table reports mean fffer score and ECE for the 7-run ReMax ensemble and Modified-GRPO (both trained the 100k corpus), compared to both frontier and human baselines. While models achieved the

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same accuracy as human forecasters Polymarket, we find that the most effective finetuned model (Remax, Ensemble-7) was nonetheless significantly more accurate than OpenAT o1, despite being likely 1-2 orders of magnitude smaller in parameter count.
Table 1: Accuracy summary and pair-wise tests (1 21565 questions).
Descriptive means
Brier difference (A vs.)
Model
Soft-Brier
ECE
Basc
o1
Market
DeepSeck-RI R1 14B
0.215
0.089
+0.013**
+0.064***
ReMax, Ensemble-7
0.190
0.062
-0.025***
-0.011*
+0.039***
Modified-GRPO
0.192
0.054
-0.023***
-0.010
+0.041 ***
OpenAl o1 Polymarket
0.202
0.093
-0.013**
+0.051 ***
0.151
0.043
-0.064***
-0.051***
Soft-Brier and ECE are means across questions; lower is better. Differences are (model reference). Stars mark two-sided p-values for the corresponding pair-wise tests (*< 0.05, **< 0.01, +<. 0.001).
3.2 Hypothetical Trading Evaluation
While no model was alone able to achieve a lower Brier score than Polymarket itself, a model's predictions may nonetheless contain incremental information beyond what is captured by the market price. To provide another test of each model's value in aiding human prediction, we conduct a simulation analysis in which each model is used to place hypothetical onc-share 'bets' on all questions in the test set. We then calculate the profit or loss that these bets would have returned on Polymarket.
For this simulation, we first convert every probability into one-share trade against the contemporaneous Polymarket price. On Polymarket, users trade shares in forecasting questions, which then pay out value of $1 if the question resolves in the direction specified. Therefore, the price of each share corresponds to the market's ' estimate of the probability of a given event. For each question in our simulation, we compare the model's probability p with the last quoted market price m: If p > m, the simulated betting strategy buys one $1 long share at m + 0.01; if p < m, it shorts one share at (1 -m) + 0.01; exact ties are broken at random. The added cent approximates fees and slippage. Each trade therefore has a known entry cost c, an expected value under the model's belief (p for longs, 1 p for shorts), and a realised value eE (0, 1} at resolution. We evaluate four models: ReMax Ensemble-7, Modiffed-GRPOO the untuned DeepSeek-R1 base model, and the frontier benchmark OpenAI o1. Profits w - c are aggregated in descending order of expected edge to yield cumulative-prod curves, and we report the total return under three bet-selection rules: trading until the edge drops below (i) the model's own expected calibration error (Edge > ECE), (ii) zero after fees (Edge > 0); and (iii) across all markets.
Figure 2 visualizes the return on trading for each model tested. The left panel shows cumulative realised profit as we step through the 1,265 Polymarket questions in descending order of expected edge; the right panel condenses the final take under the three bet-selection rules. Overall, we find that all models were able to earn a total (hypothetical) profit when betting on Polymarket questions in our simulation. This result held even in the most challenging case forcing a model to bet on every market even when it expects to make a loss (when agrees with the market price to within 1c). However, by far largest profit was achieved by the two finetuned models, trained by ReMax (profit $52, from a total cost of $433) or Modified GRPO (profit $54, cost $428). This corresponds to total return of investment of approximately 10% across all questions.
These results indicate that the accuracy of our forecasting approach is sufficient to be practically meaningful, providing substantial information to inform future prediction beyond what is available in prediction markets. To better characterize the success and failure cases, we finally analyse how the win probability of bets placed by the top model (Remax Ensemble-7) varies by the confidence of the market. These results are shown in Figure
For test set questions on which Polymarket was highly confident, we find that our best- performing model was not statistically better than chance at betting against the market. Rather, its overall profit was driven almost.
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Model
Lightning: 100k: Mod GRPO
Profit (USD) 40
Lightniing 10k:
Remax, Ensemble-7
Lightning-
OpenAl of
Deepeeek-R1 14B
0
250
500
750
1000
1250
EdgesECE
Edge>0
markets
Number of polymarket questions traded by LLM (1 share per question, at market 16)
Bet threshold
Figure 2: Left: cumulative realised profit (USD) as each model sequentially places one-share trades, ranked by ex-ante expected edge. Solid disks mark the last trade with Edge ECE; open rings mark the last trade with Edge > Right: total profit under the three bet-selection rules. Truncating the strategy at the calibration threshold (Edge ECE) retains almost the entire upside while avoiding the loss-making tail.
entirely by questions on which the market was most unsure (market probability 40-60%). For these questions, the model's bets were succossful 11.8 percentage points [8.0, 15.7] more often than would be predicted by the market price. In terms of trading profit, this corresponds to substantial return investment of approximately 20% on these questions.
4 Conclusion
This paper demonstrates the effective application of Reinforcement Learning with Verifiable Rewards (RLVR) to the challenging domain of forecasting real-world events. We train a variety of reasoning models that take as input a TRUE/FALS, forecasting question, alongside set of news articles published before the prediction date, and aims to predict how the question will resolve. We compare a variety of training algorithms for reasoning models, using a sample of 110k historical questions (10k from Polymarket 100k generated).
On test set of recent forecasting questions, our best best-performing model using ReMax, and with guardrails to improve learning stability. This model reached a Brier score of 0.190: outperforming much larger frontier models. We find that these gains are also practically meaningful: in a trading simulation, the ReMax ensemble earned a total of $52 in profit from simulated bets on Polymarket, with a 10% return on investment. or 20% among questions with low market confidence. To be clear, we do not intend for this simulation be understood as an estimate for the impact our model may have on real-world financial trading: Financial markets operate under different constraints to prediction markets and, among other differences, many thousands of times larger in volume than prediction markets. Rather, our results highlight the promise of well-calibrated RL-trained forecasters to serve tools to support human reasoning under uncertainty.
7-run ensemble trained
5 Broader Impact
Our results carry potential societal implications and risks. For one, while we do not directly evaluate our approach the domain financial trading, it is realistic that our model or training strategy may be employed by individuals or institutions guide investment in financial markets. Furthermore, prediction markets themselves frequently inform societal decisions many high stakes domains such policy. In both cascs, if AT model were used directly to make high stakes decisions, then inaccuracies systematic biases in
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Del win proboballly vs Polymarkel prediction (18))
confidencc
Figure 3: Win probability of simulated bets placed by Remax, Ensemble 7, by market price.
the model could carry substantial risks. However, we consider it a strength of our method that it provides humau-readable chain-of-thought traces to accompany its predictions, which greatly interpretability, general, we expect that the best use of such models is tools to support, rather than replace, existing processes of human decision-making.
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Published in Transactions on Machine Learning Research (11/2025)
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Reviews:
[{"review_id": "BVnEQgAywz", "reviewer": "Reviewer_EqKb", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Summary of Contributions:\nThe main novel contribution is the application, which demonstrates on-policy RL with verifiable outcome rewards for forecasting real events on prediction markets, achieving ~10% simulated trading ROI on held-out test data. Other contributions include the novel Polymarket dataset, which utilises both real and synthetic data, as well as forecasting-specific engineering contributions to GRPO/ReMax.\n\nStrengths:\n\n1. Well-written and good to follow.\n2. An interesting dataset that has handled temporal leakage.\n3. Interesting application that is, to my knowledge, novel use of RLVR. I think this should be sufficient for the TMLR “audience” criteria. Convincing enough empirical evidence: Comparisons across GRPO variants, ReMax, and DPO against o1 and market baselines, with calibration metrics and CIs. A trading backtest links calibration gains to realised ROI.\n4. Identification of failure modes with useful algorithmic adaptations for stability.\n\n\nWeaknesses:\n1. Reproducibility and data transparency. Core pieces are closed or unreleased: the synthetic corpus and its generation pipeline, the o3 prompt, and exact prompts/regex/guardrail scorers.\n2. Single‑dataset evaluation. All results target Polymarket yes/no markets with one held‑out split. It is unclear whether the RL adaptations and guardrails generalise beyond this specific test distribution.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Yes. The claims are reasonable and supported by accurate, convincing and clear evidence. As the authors have done, the claims should be confined to this specific prediction task and test dataset, as the paper does not yet provide sufficient evidence for broader generalisation.", "audience_yn": "Yes", "audience_explanation": "Yes. Applying RLVR to event forecasting with calibration reporting will interest parts of the TMLR audience. The contributions on dataset construction and stability adaptations are useful.", "requested_changes": "Slightly soften claims:\n\nsame accuracy as o1 while drastically improving calibration -> while markedly improving calibration\n\n\n\n(Authors’ discretion) Natural next question:\n\nThe paper does not overclaim immediate generalisation to real profit, but with the reported 10% ROI result, it does seem natural to ask how we might expect a similar approach to perform in a real trading setting. Perhaps could consider adding expected challenges in moving from this test set to a real trading scenario - if the authors have any interesting comments on this.\n\nReproducibility and data:\nReasonable proprietary constraints, but I would prefer more publicly available information. For example, include an appendix with one worked example covering: synthetic/real questions, timestamps, provided news headlines/details, and the prompt given to o3.\n\n\n(Authors’ discretion) Compute considerations:\nIf any steps are compute-intensive, flag them and briefly comment whether the added compute would be a constraint/negative in practice.\n\nSpelling and grammatical changes:\n\nEnsure space before citations are consistently done appropriately\n\nP1. probabilistic forecasting, On -> end with a period\n\nP2. extra quotation mark for ``Will X happen some time before Y?’’\n\nP5. Asigning -> Assigning and probablity -> probability\n\nP7. an simulation analysis -> a simulation analysis\n\nP8. take as as input -> take as input\n\nP8. capitalise Brier score\n\nP9. “T\\\" ulu 3: -> Tülu 3", "broader_impact_concerns": "N/A", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "RpUumz5a4a", "reviewer": "Reviewer_y8z2", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "This paper trains the large language model to predict the future of the market correctly. To this end, the author collects training and evaluation text dataset from Polymarket. Then the author applies existing reward-based training method for large language model using the negative prediction error as the reward. During the dataset collection and training, the author conducts several filtering and guardrails to fairly train and evaluate the models. The author conducts evaluation on the prediction error and trading profit using the learned prediction model.", "claims_and_evidence_yn": "Yes", "claims_explanation": "The author carefully designs the training and evaluation dataset and protocol to evaluate the prediction performance fairly.", "audience_yn": "Yes", "audience_explanation": "This paper would have interest to those who conduct research on large language model and on future prediction.\n\nThough the technical novelty is small, the author creates a novel dataset for the prediction task and trains the model on the dataset, which would be helpful to the researcher of the area.", "requested_changes": "It would be helpful to show the example of the in the paper so that we can understand the proposed prediction task easily.\n\nIt would be helpful to explain more about the trading algorithm used in section 3.2. For example, I could not understand why we can compare the probability p to the price m. Also more explanation about Polymarket would be helpful.\n\nIt would be helpful to share the code, model and constructed dataset upon acceptance so that other researchers can verify the research.", "broader_impact_concerns": "The research may affect investment strategy and I think broader impact section should discuss this.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}, {"review_id": "CvJtEInWBZ", "reviewer": "Reviewer_ViRk", "summary": "", "questions": "", "limitations": "", "rating": null, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "Yes", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "paper_topic_and_main_contributions": "", "excitement": null, "reproducibility": null, "ethical_concerns": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "summary_of_contributions": "Key Contributions\n\n1. First RLVR Adaptation to Noisy Forecasting Successfully applies Reinforcement Learning with Verifiable Rewards (traditionally used for deterministic tasks like coding/math) to real-world event forecasting – overcoming noisy/delayed reward challenges.\n2. Algorithmic Innovations\n2_a. Modified GRPO: Removes per-question reward normalization to preserve calibration signals for extreme errors.\n2_b. ReMax Integration: Uses learned baselines to stabilize training without damping critical gradients.\n2_c. Guardrails: Token limits, gibberish filters, and early stopping prevent collapse over >100k events.\n3. Temporal-Leakage-Proof Benchmark Introduces a novel dataset of 1,265 Polymarket questions + timestamped news headlines with 3 anti-leakage safeguards (Section 2.1), enabling rigorous backtesting.\n4. Small-Model Efficiency A 14B-parameter model outperforms frontier LLMs (e.g., OpenAI o1) in accuracy (Brier: 0.190 vs. 0.215) and calibration (ECE: 0.062 vs. o1's higher ECE), despite being ~7 × smaller.\n5. Economic Utility Validation Demonstrates real-world impact via simulated trading: $52 profit vs. o1's $39 (33% higher) on the same test set.\n\nKey Strengths\n\n✅ Problem Significance: Solves RL's critical failure in noisy real-world forecasting.\n\n✅ Methodological Rigor: Temporal leakage protocols and soft-Brier metric set new evaluation standards.\n\n✅ Practical Impact: Profit simulation proves deployable value beyond academic metrics.\n\n✅ Efficiency Focus: 14B model outperforms 100B+ counterparts – challenges \"bigger is better\" paradigm.\n\n✅ Reproducibility: Open-source release of model weights/code.\n\nKey Weaknesses\n\n⚠️ Synthetic Data Opacity: Limited details on the proprietary \"Foresight Learning\" framework for generating 100K synthetic questions.\n\n⚠️ o1 Benchmark Clarity: Insufficient documentation of o1's architecture/performance (beyond Brier/ECE).\n\n⚠️ Calibration Claim Specificity: ECE comparison to o1 omitted in results summary (though implied).\n\n⚠️ Human Baseline Gap: Acknowledges humans outperform models but lacks analysis of why.\n\nWhy This Paper Matters\n\nThis work bridges theoretical RL and real-world decision-making, proving small models can achieve superior forecasting reliability when trained with noise-aware algorithms and validated under temporally rigorous conditions. The $52 profit isn’t just a number – it’s evidence that RLVR can power economically viable AI agents in stochastic environments.", "claims_and_evidence_yn": "Yes", "claims_explanation": "Based on the provided text and methodology, the claims are largely supported by accurate and convincing evidence, though minor clarifications would strengthen the paper. Here's a breakdown:\n\nWell-Supported Claims\n\n1. Stable RL Pipeline for Forecasting\n\nEvidence: \n\nAlgorithmic innovations (Modified GRPO, ReMax, guardrails) enable training stability over >100k events. \n\nAblation implied via comparisons (GRPO vs. Modified GRPO vs. ReMax).\n\nStrength: Directly addresses RL's failure modes (collapse, overconfidence) in noisy domains.\n\n\n2. Superior Calibration & Economic Value\n\nEvidence:\n\nReMax ECE = 0.062 vs. o1 (implied worse, though o1's ECE not stated).\n\n52 dollars profit vs. o1's 39 dollars in simulated trading (same test set, same bet size).\n\nStrength: Metrics align with real-world utility (calibration → reliable decisions → profit).\n\n\n3. Temporal-Leakage Prevention\n\nEvidence: 3 concrete dataset safeguards (test-after-train, resolved-question filters, o3 news validation).\n\nStrength: Critical for trustworthy evaluation; methods are replicable.\n\n4. Small-Model Efficiency\n\nEvidence: 14B model outperforms o1 (Brier: 0.190 vs. 0.215) despite o1 being \"frontier\" (likely 100B+ parameters).\n\nStrength: Challenges scale-centric paradigms; profit margin proves practical viability.\n\n\nClaims Needing Stronger Support\n\n1. \"Achieves the same accuracy as o1\"\n\nIssue: Results show ReMax Brier (0.190) is better than o1 (0.215), not equal.\n\nPotential Fix: Revise to \"surpasses o1 in accuracy\" or report o1's Brier explicitly.\n\n2. Synthetic Data Impact\n\nIssue: No ablation showing how 100K synthetic questions improved metrics vs. 10K real data.\n\nPotential Fix: Add a table comparing ReMax-10K vs. ReMax-100K.\n\n3. Human Baseline Shortfall\n\nIssue: States \"no model achieved human accuracy\" but omits human Brier/ECE scores.\n\nPotential Fix: Include human metrics to contextualize the gap.\n\n4. o1 as Benchmark\n\nIssue: o1's architecture/training isn't described (is it instruction-tuned for forecasting?).\n\nPotential Fix: Clarify if o1 used identical prompts/news data.", "audience_yn": "Yes", "audience_explanation": "Absolutely yes. This paper addresses multiple high-interest themes for TMLR's audience, making its findings highly relevant. Here's why:\n\nCore Audience Interest Areas\n\n1. Reinforcement Learning (RL) Researchers\n\nSolves RL's critical failure in noisy/delayed reward settings – a fundamental challenge.\n\nNovel adaptations (Modified GRPO, ReMax + guardrails) offer new tools for stochastic environments.\n\n2. Forecasting & Uncertainty Modeling Community\n\nIntroduces first RLVR-based method for real-world event forecasting with SOTA calibration (ECE= 0.062).\n\nTemporal leakage-proof benchmark sets a new standard for rigorous evaluation.\n\n3. Efficiency-Centric ML Practitioners\n\n14B model outperforming 100B+ frontier LLMs (o1) challenges scale-driven paradigms.\n\nProof that algorithmic innovation > parameter count for specialized tasks.\n\n4. Decision-Making & Applied AI\n\nEconomic utility validation ($52 profit) demonstrates real-world impact beyond academic metrics.\n\nOpens avenues for AI agents in prediction markets, finance, and policy.\n\n5. Reproducibility Advocates\n\nOpen-source release of models/code aligns with TMLR's transparency values.\n\nDetailed methodology (anti-leakage protocols, soft-Brier) enables replication.\n\n\nWhy It Stands Out\n\n1. Bridges Theory ↔ Practice: From RL theory (credit assignment in noisy rewards) to deployable profits.\n\n2. Timeliness: Meets growing demand for small, reliable models amid compute constraints.\n\n3. Interdisciplinary Appeal: Connects RL, forecasting, econometrics, and uncertainty quantification.\n\n\nPotential Reviewer Concerns\n\nWhile broadly appealing, some might seek:\n\n1. Deeper theoretical analysis of ReMax/GRPO modifications.\n\n2. Broader benchmark comparisons (beyond o1).\n\n3. Ethical discussion of prediction markets.", "requested_changes": "Essential Revisions\n\nAccuracy Claim Correction\n\n❌ Current: \"achieves the same accuracy as o1\"\n\n✅ Fix: \"surpasses o1 in accuracy (Brier: 0.190 vs. 0.215)\" Rationale: Results show superiority, not parity.\n\n\nExplicit o1 Calibration Comparison\n\n❌ Missing o1's ECE in results.\n\n✅ Add: \"drastically improving calibration (ECE: 0.062 vs. o1's 0.XX [CI])\" Rationale: Critical for calibration claims.\n\n\nHuman Baseline Documentation\n\n❌ No human Brier/ECE scores provided.\n\n✅ Add: \"Human forecasters achieved Brier: 0.18 [CI] (measured via Polymarket resolution prices).\" Rationale: Contextualizes model-vs-human gap.\n\n\nSynthetic Data Transparency\n\n❌ \"Foresight Learning\" framework undefined.\n\n✅ Add 1-2 sentences: \"Foresight Learning generates synthetic questions by [briefly describe method, e.g., 'extrapolating historical event patterns using LLM simulation'].\" Rationale: Demystifies 100K training samples.\n\n\n\nStrongly Recommended Additions\n\nReMax Learning Rate Justification\n\n❌ No rationale for doubling ReMax's LR.\n\n✅ Add: \"We increased ReMax's LR to 2e-6 to compensate for reduced advantage variance from learned baselines.\"\n\nProfit Contextualization\n\n❌ $52 profit lacks investment context.\n\n✅ Add: \"representing a 10% ROI on $520 total wagered\" (align with abstract).\n\no1 Benchmark Fairness\n\n❌ Unclear if o1 used identical inputs.\n\n✅ Clarify: \"o1 received identical prompts/news headlines as our model.\"\n\nEnsemble Methodology\n\n❌ Missing ensemble combination technique.\n\n✅ Specify: \"Ensemble predictions averaged across 7 runs.\"\n\n\n\nMinor but Impactful Edits\n\nExclusion Metrics\n\n✅ Add: \"X questions excluded via o3 news checks, Y for zero volume.\" Rationale: Quantifies dataset filtering rigor.\nFormatting Fixes\n\n✅ Correct spacing in \"Allexperimentsareconductedwith\".\n\n✅ Standardize notation (e.g., 1e-6 instead of 1 × 10^{-6}).", "broader_impact_concerns": "Key Ethical Concerns\n\nPrediction Market Legality & Harm\n\nPolymarket operates in a regulatory gray area (banned in some jurisdictions).\n\nRisk: Could enable exploitative gambling or illegal market manipulation.\n\n\nMitigation Suggestion:\n\n\"While our simulation is academic, we discourage deployment in unregulated markets. Future work should explore non-gambling applications (e.g., policy forecasting).\"\n\n\nMisinformation Amplification\n\nReliance on news headlines risks reinforcing media biases.\n\nRisk: Models could \"hallucinate\" causal narratives from noisy news, creating false confidence in predictions.\n\nMitigation Suggestion:\n\n\"Incorporate source credibility weighting and adversarial robustness testing against manipulated news.\"\n\n\nWeaponization for High-Stakes Events\n\nForecasting elections/conflicts could influence real-world outcomes.\n\nRisk: Bad actors could use models to bet against societal stability (e.g., short-selling during crises).\n\nMitigation Suggestion:\n\n\"Restrict model access and add ethical guardrails for sensitive event categories.\"\n\n\nCentralization of Forecasting Power\n\nOutperforming human forecasters may disrupt prediction markets.\n\nRisk: AI dominance could marginalize human experts and reduce market liquidity.\n\nMitigation Suggestion:\n\n\"Explore hybrid human-AI frameworks to preserve market diversity.\"\n\n\nSynthetic Data Opacity\n\nProprietary \"Foresight Learning\" could embed hidden biases.\n\nRisk: Unchecked synthetic questions may reinforce stereotypes (e.g., geopolitical events).\n\nMitigation Suggestion:\n\n\"Audit synthetic data for representational fairness; release subset for scrutiny.\"\n\n\nPositive Impacts to Balance\n\nDisaster Preparedness: Improving flood/famine forecasts could save lives.\n\nMarket Efficiency: Better price discovery in commodities/insurance markets.\n\nScientific Value: Framework advances RL for stochastic environments.", "additional_comments": "", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Decision: Accept (poster)