Marrying Pricing and Advertising with LLMs

Alessandro Barro; Francesco Bacchiocchi; Francesco Emanuele Stradi; Alberto Marchesi

cs.GTOct 7, 2026

Marrying Pricing and Advertising with LLMs

Authors: Alessandro Barro, Francesco Bacchiocchi, Francesco Emanuele Stradi, Alberto Marchesi

Organizations: Politecnico di Milano

Abstract

We study a sequential pricing problem in which a seller jointly posts a price and an advertisement generated by a large language model (LLM). The seller aims to maximize revenue under an unknown product demand that depends on both decisions, while observing only whether each offer leads to a purchase. We propose an online actor-critic algorithm that combines low-rank adaptation (LoRA) of a pretrained LLM with a demand model fitted to available data. At each round, the actor generates an advertisement, and the critic estimates purchase probabilities to guide price selection. Then, the resulting feedback is used to update both the actor and the critic, with the critic's revenue estimates providing a baseline for policy gradient updates of the actor. To evaluate our approach, we develop an evaluation framework with three synthetic demand models and a demand simulator built from real-world marketplace data. Finally, we compare our algorithm with benchmarks that do not jointly optimize price selection and advertisement generation, achieving expected revenue gains over the reference policy of 5.69%, 5.18% and 55.96% under the three synthetic demand models and 5.81% under the marketplace simulator.

Figures & tables

p_{\tau,b}\in\displaystyle\arg\max_{p\in[0,1]}p\,\hat{d}_{\phi_{\tau}}(p,x_{\tau,b},z)

Algorithm 1 Pricing & Advertising via Low-Rank Adaptation and REINFORCE Leave-One-Out

Figure 1: One round of seller-buyer interaction. The actor generates an advertisement, the seller uses the critic to select a price, and the buyer provides purchase feedback.

Policy / metric	Logit	Probit	Price disclosure
Trained	0.217117	0.205616	0.027162
Reference	0.205418	0.195496	0.017416
$\bm{\Delta u}$	+0.011698	+0.010120	+0.009746
$\bm{\Delta u(\%)}$	+5.69%	+5.18%	+55.96%
95% interval for $\Delta u$	[0.0111, 0.0123]	[0.0095, 0.0107]	[0.0096, 0.0099]

Table 1: Synthetic expected revenue from 10,000 fresh advertisements per policy and environment. The 95% intervals use 2,000 bootstrap resamples, drawn independently for the compared policies.

Figure 2: Synthetic evaluation. Top: held-out mean revenues ( Reference , horizontal; Trained , vertical), with a dashed equality line. Each point averages 100 independently generated advertisements per policy; independent blocks are aligned for display only. Bottom: trailing ten-batch revenue means for Trained (blue) and UCB (orange). Trained revenue uses recorded offer probabilities; UCB revenue is estimated from logged prices and feature frequencies (Appendix B.2 ).

Policy / metric	Audio / Video	Home Appliances	Laptops	Mobile Phones	Tablets / E-readers	Overall
Trained	0.2363	0.2446	0.1802	0.1936	0.1987	0.2107
Reference	0.2303	0.2329	0.1577	0.1898	0.1848	0.1991
$\bm{\Delta u}$	+0.0060	+0.0117	+0.0225	+0.0038	+0.0139	+0.0116
$\bm{\Delta u(\%)}$	+2.59%	+5.01%	+14.26%	+1.98%	+7.55%	+5.81%
95% interval for $\Delta u$	$[0.0036,$ $0.0083]$	$[0.0091,$ $0.0143]$	$[0.0172,$ $0.0285]$	$[0.0019,$ $0.0057]$	$[0.0115,$ $0.0163]$	$[0.0097,$ $0.0136]$

Table 2: Marketplace expected revenue from 100 fresh advertisements per policy and product. The 95% intervals use 5,000 bootstrap resamples, drawn over products and paired across the policies.

Figure 3: Marketplace evaluation. Upper left: each point shows mean expected revenue for one test product ( Reference , horizontal; Trained , vertical), with a dashed diagonal line indicating equal revenue. Markers follow the category order in Table 2 : circle, square, upward triangle, diamond, downward triangle. Other panels: training-revenue curves, which use the same colors as in Figure 2 .

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Quantity	Value
Actor	Qwen2.5-1.5B-Instruct
Adapted matrices	Query and value projections; $L=56$ across 28 layers
LoRA rank / scaling coefficient	$r_{\ell}=8$ / $\alpha_{\ell}=16$ for every $\ell$
Effective weight update	$(\alpha_{\ell}/r_{\ell})B_{\ell}A_{\ell}=2B_{\ell}A_{\ell}$
Query adapter dimensions	$A_{\ell}\in\mathbb{R}^{8\times 1536}$ , $B_{\ell}\in\mathbb{R}^{1536\times 8}$
Value adapter dimensions	$A_{\ell}\in\mathbb{R}^{8\times 1536}$ , $B_{\ell}\in\mathbb{R}^{256\times 8}$

Appendix

Table 3: Shared implementation settings across synthetic and marketplace experiments. Appendix B.4 specifies changes to initial critic support, exploration, and anchoring in the offline-data ablation.

Condition	$0.99	$2.99	$5.99
Plain Ad, $h=0$	0.106	0.024	0.011
Price Ad, $h=1$	0.147	0.039	0.012

Appendix

Table 4: Price disclosure purchase probabilities from Table A5, Panel A of Dubé et al. (2026) . Plain Ad and Price Ad demand are interpolated separately over the three observed dollar prices.

Demand	Policy	Revenue	Price	Purchase prob.	Feature rate
Logit	Trained	0.217117	0.555954	0.390138	0.971100
Logit	Reference	0.205418	0.534996	0.381832	0.821400
Probit	Trained	0.205616	0.647711	0.317174	0.967300
Probit	Reference	0.195496	0.637498	0.305357	0.821400
Price disclosure	Trained	0.027162	0.417170	0.065257	0.982300
Price disclosure	Reference	0.017416	0.469808	0.038771	0.351700

Appendix

Table 5: Synthetic test means over 10,000 advertisements per policy and environment. Prices are normalized; the feature indicates durable in logit/probit and the disclosure token in price disclosure.

Figure 5: Marketplace held-out revenues for the 100 test products ( Reference , horizontal; Trained , vertical), with category-specific markers. Each coordinate averages 100 advertisements per policy and product; the dashed diagonal line indicates equal expected revenue.

Category	$\Delta u$	95% interval for $\Delta u$	Improved products
Audio/Video	+0.005956	[0.003590, 0.008313]	16/20
Home Appliances	+0.011678	[0.009055, 0.014272]	20/20
Laptops	+0.022490	[0.017165, 0.028486]	20/20
Mobile Phones	+0.003765	[0.001890, 0.005677]	15/20
Tablets/E-readers	+0.013943	[0.011474, 0.016290]	20/20
Overall	+0.011566	[0.009672, 0.013632]	91/100

Appendix

Table 6: Marketplace revenue gains and improved-product counts for Trained over Reference . The 95% intervals use 5,000 paired-product bootstrap resamples.

Figure 6: Trained expected revenue as initial critic data decrease from 100% to 0%, using the exploration schedule in Equation 19 . Points average the same 20 held-out Laptop products; the error bars show 95% product-bootstrap intervals conditional on one training run per data budget.

Initial data	All listings	Laptop listings	Uniform offers	Revenue	95% interval
100%	7,291	190	0	0.180224	[0.1624, 0.1990]
75%	5,468	142	342	0.187076	[0.1743, 0.2004]
50%	3,645	95	703	0.189475	[0.1764, 0.2028]
25%	1,823	48	1,068	0.184210	[0.1705, 0.1982]
0%	0	0	1,409	0.167030	[0.1490, 0.1854]

Appendix

Table 7: Initial critic training data, offers sampled from the uniform exploration distribution and Trained expected revenue with 16,000 online outcomes. The 95% intervals use 5,000 bootstrap resamples of the 20 held-out Laptop products.

Figure 7: Baseline and revenue-advantage MSE ratios for critic-based versus observed-reward estimators. Left: baseline MSE as offline support decreases, on a logarithmic scale. Right: advantage MSE at full data, including purchase noise from the offer whose advantage is estimated. The dashed line indicates equal conditional MSE.

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Abstract

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