MIRT: Transformers for Truthful Generative Auctions with Whole-feed Permutation Externalities

Ali Elahi; Ermis Soumalias; Jason Cheuk Nam Liang; Daniel Yao; Michael J. Curry

cs.GTOct 5, 2026

MIRT: Transformers for Truthful Generative Auctions with Whole-feed Permutation Externalities

Authors: Ali Elahi, Ermis Soumalias, Jason Cheuk Nam Liang, Daniel Yao, Michael J. Curry

Organizations: University of Illinois Chicago · Meta

Abstract

Modern online platforms commonly rank ads and organic content separately before blending them into a feed displayed to the user, overlooking externalities: an item's click-through rate depends on its surrounding content, not only on its own position. Recent learning-based feed generation mechanisms model some of these cross-type interactions to globally optimize for the whole feed's welfare. However, these approaches either fix the ordering of organic content, or lack exact strategyproofness guarantees for bidders. To combat these shortfalls, we introduce the Maximal-in-Range Transformer (MIRT) mechanism class, which uses a transformer to generate a range of candidate feeds that jointly order ads and organic content, and selects the welfare-maximizing feed in the range. However, there is a tension: strategyproofness requires the generated range to be bid-independent, even though a candidate feed's welfare depends linearly on the bids. Our key technical contribution is a reinforcement learning approach that incorporates both candidate generation and bid-aware selection into training, enabling a bid-independent transformer to learn to generate high-welfare ranges by accounting for both individual feed quality and the collective quality of the range. Additionally, we bound the pseudo-dimension of the MIRT class under hard attention, showing that near-optimal expected welfare is learnable with sample complexity polynomial in the transformer size and only logarithmic in the range size. Empirically, MIRT outperforms the previous non-strategyproof state-of-the-art feed models while remaining exactly strategyproof. Our results show that transformer-based auctions can deliver externality-aware whole-feed optimization without sacrificing exact incentive compatibility, removing a major obstacle to their practical deployment.

Figures & tables

Figure 1: Schematic diagram of the MIRT architecture.

Figure 2: Performance in the reference environment. Box-plot with medians/spread for test contexts for one trained model. The first two panels show per-context percentage lift over Random+MIR in total welfare and total transfer. The final panel shows ex-post regret as a percentage. MIRT used sampling temperature 2.4, and CGA/NGA used

\rho=1000.

MIRT achieves higher total welfare than CGA and NGA, and has zero regret by construction.

Externality	Prev. Organic	Additive	Activation	Attention	Multiplicative	Topic	Position
Random+MIR	$27.18\pm 0.214$	$27.34\pm 0.215$	$29.67\pm 0.227$	$28.50\pm 0.220$	$27.49\pm 0.216$	$27.18\pm 0.214$	$27.33\pm 0.214$
Greedy+MIR	$30.71\pm 0.239$	$30.83\pm 0.240$	$33.24\pm 0.255$	$31.93\pm 0.245$	$30.91\pm 0.242$	$30.63\pm 0.237$	$30.93\pm 0.241$
MIRT $(K=32)$	$32.11\pm 0.245$	$31.80\pm 0.243$	$33.92\pm 0.257$	$32.41\pm 0.247$	$33.00\pm 0.254$	$31.87\pm 0.247$	$32.86\pm 0.250$
MIRT $(K=256)$	$32.50\pm 0.246$	$32.20\pm 0.245$	$34.47\pm 0.258$	$32.86\pm 0.248$	$33.49\pm 0.256$	$32.34\pm 0.249$	$33.30\pm 0.252$
CGA	$31.08\pm 0.238$	$31.37\pm 0.241$	$33.55\pm 0.254$	$32.56\pm 0.247$	$31.35\pm 0.241$	$31.20\pm 0.239$	$31.15\pm 0.239$
NGA	$31.09\pm 0.238$	$31.33\pm 0.240$	$33.51\pm 0.254$	$32.59\pm 0.247$	$31.37\pm 0.241$	$31.23\pm 0.239$	$31.16\pm 0.239$

Table 1: Mean (

\pm

approximate 95% CI) absolute total welfare across held-out contexts under each externality function with default problem size and bid distribution. Highlighted cells are the highest-performing mechanisms. Corresponding total transfer is in Appendix Table 4 . This table was generated with 40 epochs of training for each MIRT model, and sampling temperature 1 (except for the Prev. Organic externality, which used 2.4). CGA/NGA used

\rho=1.

	Social Welfare				Total Transfer
Distribution	Exponential	Uniform	Lognormal	Pareto	Exponential	Uniform	Lognormal	Pareto
Random+MIR	$27.15\pm 0.214$	$34.27\pm 0.222$	$27.33\pm 0.205$	$44.86\pm 0.761$	$2.05\pm 0.039$	$4.83\pm 0.073$	$2.47\pm 0.040$	$5.60\pm 0.093$
Greedy+MIR	$30.71\pm 0.240$	$39.83\pm 0.257$	$31.38\pm 0.227$	$50.59\pm 0.781$	$1.44\pm 0.023$	$3.29\pm 0.048$	$1.93\pm 0.026$	$3.72\pm 0.058$
MIRT $(K=32)$	$32.06\pm 0.245$	$42.67\pm 0.268$	$32.69\pm 0.230$	$53.49\pm 0.882$	$2.23\pm 0.035$	$5.55\pm 0.075$	$2.76\pm 0.032$	$5.05\pm 0.073$
MIRT $(K=256)$	$32.52\pm 0.246$	$43.32\pm 0.269$	$32.95\pm 0.231$	$55.02\pm 0.916$	$2.76\pm 0.037$	$7.14\pm 0.081$	$3.75\pm 0.036$	$6.64\pm 0.076$
CGA	$31.08\pm 0.238$	$40.37\pm 0.252$	$31.19\pm 0.226$	$51.00\pm 0.767$	$3.26\pm 0.024$	$6.35\pm 0.024$	$3.29\pm 0.011$	$3.25\pm 0.015$

Table 2: Mean (

\pm

CI across held-out contexts) absolute total welfare and total transfer across held-out contexts under each bid prior and default problem size and externality. Highlighted cells are the highest-performing mechanisms. Results in this table were generated with 40 epochs of training for each MIRT model, with temperature

2

. CGA/NGA have

\rho=1000

Figure 3: Scaling of performance with the size of the range.

Appendix figures & tables7 assets

Supplementary material from the paper’s appendix.

Appendix

Externality function	Parameter values
Additive Similarity	$\eta=0.5$ , $\lambda=0.7$ , $w=4$
Neighborhood Activation	$\eta=0.5$ , $\tau_{\mathrm{act}}=0.3$ , $w=4$
Softmax Attention	$\eta=0.5$ , $\tau_{\mathrm{sm}}=0.5$ , $\lambda=0.7$ , $w=4$
Multiplicative interactions	$\eta=0.5$ , $\lambda=0.7$ , $w=4$
Topic affinity	$\eta=0.5$ , $\lambda=0.7$ , $w=4$ , $K=20$ topics
Position-modulated	$\eta_{\mathrm{above}}=0.6$ , $\eta_{\mathrm{below}}=0.2$

Appendix

Table 3: Default parameter values used in all experiments.

Figure 4: Welfare distributions for the default environment. Generated over 2,000 contexts with 256 random feasible feeds each. From left to right: (1) ad bid–quality products and organic benefits; (2) welfare per feed; (3) within-context standard deviation across feeds; (4) within-context maximum minus minimum among sampled feeds. Blue denotes advertiser quantities and green denotes organic quantities.

Figure 5: This figure shows the variation in performance of optimizing the softmax sampling temperature at test time on frozen models. For models trained on welfare, a higher temperature results in decreased welfare and increased total transfer.

Figure 6: Results of training models to optimize a virtual welfare objective instead of welfare. MIR methods use Myerson transfers instead of VCG transfers. MIRT has a sampling temperature of 1, and CGA/NGA have

\rho=1000.

Method	Prev. Organic	Additive	Activation	Attention	Multiplicative	Topic	Position
Random+MIR	$2.01\pm 0.04$	$2.06\pm 0.04$	$2.74\pm 0.05$	$2.36\pm 0.05$	$2.13\pm 0.04$	$2.00\pm 0.04$	$2.08\pm 0.04$
Greedy+MIR	$1.43\pm 0.02$	$1.42\pm 0.02$	$1.74\pm 0.03$	$1.58\pm 0.03$	$1.43\pm 0.02$	$1.40\pm 0.02$	$1.47\pm 0.02$
MIRT $(K=32)$	$2.13\pm 0.03$	$2.06\pm 0.03$	$2.25\pm 0.04$	$2.03\pm 0.03$	$2.28\pm 0.04$	$2.20\pm 0.04$	$2.22\pm 0.04$
MIRT $(K=256)$	$2.64\pm 0.04$	$2.52\pm 0.04$	$2.78\pm 0.04$	$2.58\pm 0.04$	$2.81\pm 0.04$	$2.73\pm 0.04$	$2.72\pm 0.04$
CGA	$4.93\pm 0.04$	$3.89\pm 0.02$	$4.20\pm 0.03$	$4.51\pm 0.03$	$5.13\pm 0.04$	$4.35\pm 0.03$	$4.69\pm 0.03$
NGA	$4.32\pm 0.03$	$4.60\pm 0.03$	$5.24\pm 0.04$	$5.75\pm 0.04$	$4.85\pm 0.04$	$4.51\pm 0.03$	$5.12\pm 0.04$

Appendix

Table 4: Mean (

\pm

CI across held-out contexts) absolute total transfer across held-out contexts under each externality function with default problem size and bid distribution. Highlighted cells are the best-performing among mechanisms. Results in this table for all columns were generated using MIRT models trained for 40 epochs with a temperature of 1. CGA/NGA have

\rho=1

, resulting in 10-16% regret.

	$(N_{O}{=}12,\ M{=}8,\ T{=}12)$ 3 ads, 9 posts		Default $(N_{O}{=}18,\ M{=}10,\ T{=}24)$ 6 ads, 18 posts		$(N_{O}{=}36,\ M{=}18,\ T{=}36)$ 9 ads, 27 posts
Method	Welfare	Total Transfer	Welfare	Total Transfer	Welfare	Total Transfer
Random+MIR	$17.838\pm 0.105$	$2.155\pm 0.039$	$27.155\pm 0.214$	$2.047\pm 0.039$	$35.043\pm 0.125$	$2.785\pm 0.057$
Greedy+MIR	$20.048\pm 0.122$	$1.810\pm 0.029$	$30.708\pm 0.240$	$1.437\pm 0.023$	$44.619\pm 0.172$	$2.102\pm 0.035$
MIRT $(K{=}32)$	$20.885\pm 0.128$	$2.585\pm 0.037$	$32.020\pm 0.244$	$2.258\pm 0.036$	$46.882\pm 0.182$	$3.025\pm 0.044$
MIRT $(K{=}256)$	$21.346\pm 0.131$	$3.077\pm 0.040$	$32.500\pm 0.246$	$2.799\pm 0.037$	$47.904\pm 0.186$	$4.017\pm 0.048$
CGA	$20.222\pm 0.117$	$1.955\pm 0.013$	$31.084\pm 0.238$	$3.125\pm 0.021$	$47.076\pm 0.172$	$6.484\pm 0.050$

Appendix

Table 5: Absolute total welfare and transfer (mean

\pm

CI across held-out contexts) across different problem sizes, trained under the reference configuration. MIRT used a decoding temperature of 2.4, and CGA/NGA used

\rho=1000.

	Organic Welfare		Advertiser Welfare		Total Welfare		Total Transfer		Regret ( $\Psi$ )
Method	Mean $\pm$ CI	Median	Mean $\pm$ CI	Median	Mean $\pm$ CI	Median	Mean $\pm$ CI	Median	Mean $\pm$ CI	Median
Random+MIR	$18.937\pm 0.202$	$17.307$	$8.217\pm 0.097$	$7.362$	$27.155\pm 0.214$	$25.739$	$2.047\pm 0.039$	$1.687$	$0.000\pm 0.000$	$0.000$
Greedy+MIR	$20.752\pm 0.217$	$19.089$	$9.956\pm 0.112$	$8.975$	$30.708\pm 0.240$	$29.177$	$1.437\pm 0.023$	$1.237$	$0.000\pm 0.000$	$0.000$
MIRT (32)	$20.554\pm 0.214$	$18.877$	$11.466\pm 0.124$	$10.412$	$32.020\pm 0.244$	$30.486$	$2.258\pm 0.036$	$1.949$	$0.000\pm 0.000$	$0.000$
MIRT (256)	$20.562\pm 0.214$	$18.910$	$11.938\pm 0.128$	$10.865$	$32.500\pm 0.246$	$30.904$	$2.799\pm 0.037$	$2.491$	$0.000\pm 0.000$	$0.000$
CGA	$20.915\pm 0.217$	$19.239$	$10.169\pm 0.112$	$9.215$	$31.084\pm 0.238$	$29.558$	$3.125\pm 0.021$	$3.006$	$0.105\pm 0.002$	$0.085$

Appendix

Table 6: Absolute metrics across methods for the reference configuration as described in Section 5 . Means with approximate 95% confidence intervals across held-out test contexts in the test set, alongside medians. Results in this table were generated with 40 epochs of training for each MIRT model with inference time temperature

2.4

. For CGA/NGA,

\rho=1000

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