From Data to Decisions: Automating Business Rules with AI

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Author: Denis Avetisyan

A new framework leverages the power of deep learning and optimization techniques to translate complex retail data into actionable strategies for pricing and product selection.

DeepRule establishes a framework for dissecting complex systems by systematically probing boundaries and exploiting inherent contradictions to reveal underlying mechanisms.
DeepRule establishes a framework for dissecting complex systems by systematically probing boundaries and exploiting inherent contradictions to reveal underlying mechanisms.

DeepRule integrates large language models, symbolic regression, and constrained optimization for improved assortment and pricing decisions.

Existing theoretical models often struggle to capture the complexities of real-world retail economics, creating a misalignment between strategy and outcome. This paper introduces ‘DeepRule: An Integrated Framework for Automated Business Rule Generation via Deep Predictive Modeling and Hybrid Search Optimization’-a novel approach integrating large language models, symbolic regression, and constrained optimization to bridge this gap. By fusing unstructured data with multi-agent dynamics, DeepRule generates interpretable pricing and assortment strategies demonstrably superior to traditional baselines. Could this framework unlock a new era of data-driven, economically intelligent decision-making in complex business environments?

Deconstructing Demand: The Flaws in Conventional Pricing

Conventional pricing strategies, often reliant on cost-plus markup or simple competitor-based approaches, increasingly fail to capture the intricate dynamics of contemporary markets. These models struggle to account for factors like fluctuating consumer demand, the impact of promotions, or the subtle influence of external events – ultimately leading to suboptimal pricing decisions. Consequently, businesses experience lost revenue opportunities as products are either underpriced, leaving money on the table, or overpriced, resulting in decreased sales volume and increased inventory holding costs. This inefficiency extends to inventory management, where inaccurate demand forecasting, driven by flawed pricing assumptions, can lead to both stockouts – frustrating customers and losing sales – and excess inventory, tying up capital and increasing the risk of obsolescence. A shift towards more responsive and data-driven pricing is therefore crucial for maximizing profitability and maintaining a competitive edge.

Traditional approaches to product assortment often rely on fixed selections, failing to account for the intricate interplay of consumer demand, seasonal trends, and the competitive landscape. This static methodology overlooks crucial factors – a summer surge in demand for grilling equipment, for instance, or a competitor’s promotional pricing on a similar item – leading to missed revenue opportunities and potential inventory imbalances. Consequently, retailers may find themselves overstocked with items that aren’t currently appealing, while simultaneously experiencing shortages in high-demand products. Modern consumers exhibit increasingly dynamic preferences, necessitating an assortment strategy that’s responsive, adaptable, and capable of anticipating shifts in the market to deliver the right products, at the right time, and in the right quantities.

The limitations of conventional, rule-based pricing and assortment strategies are becoming increasingly apparent in today’s volatile markets. These systems, often reliant on pre-defined margins or fixed product selections, struggle to respond effectively to fluctuating demand, competitive shifts, and individual customer preferences. A transition towards adaptive, data-driven solutions is therefore essential for sustained success. These advanced systems leverage real-time data analysis, machine learning algorithms, and predictive modeling to continuously optimize both pricing and product assortments. By dynamically adjusting to market conditions and consumer behavior, businesses can maximize revenue, minimize waste, and cultivate stronger customer relationships – moving beyond static plans to a state of continuous, intelligent adaptation.

Unlocking greater revenue potential demands a shift towards dynamic price and assortment strategies powered by advanced optimization and artificial intelligence. Rather than relying on static, predetermined approaches, these techniques enable businesses to respond in real-time to fluctuating consumer demand, competitive pressures, and seasonal trends. Sophisticated algorithms can analyze vast datasets – encompassing purchase history, browsing behavior, and external factors like weather – to predict optimal pricing for individual products and curate assortments tailored to specific customer segments. This granular level of control allows for maximized profit margins, reduced inventory waste, and increased customer satisfaction, ultimately moving beyond reactive strategies to a proactive, data-driven approach to revenue management. The result is a more agile and responsive business capable of capitalizing on market opportunities as they arise, creating a sustainable competitive advantage.

Different search methods were evaluated to determine optimal assortment-pricing rules.
Different search methods were evaluated to determine optimal assortment-pricing rules.

The Mathematical Foundation: Core Algorithms for Dynamic Control

Mixed Integer Programming (MIP) is a mathematical optimization technique frequently employed in dynamic pricing strategies due to its capacity to handle both continuous and discrete variables, representing factors like price points and inventory levels. Formally, a MIP problem seeks to minimize or maximize a linear objective function subject to linear and integer constraints. These constraints can model complex business rules, such as capacity limits, minimum and maximum price thresholds, and relationships between different products or services. The resulting solution provides an optimal pricing strategy that satisfies all defined constraints while achieving the desired business objective, typically maximizing revenue or profit. Solving MIP problems often involves algorithms like Branch and Bound or Cutting Plane methods, which can be computationally intensive but yield provably optimal results for many dynamic pricing scenarios.

Approximation algorithms, specifically heuristics, are essential for deploying optimization solutions at scale. While exact methods like Mixed Integer Programming guarantee optimal solutions, their computational complexity often becomes prohibitive as problem size increases. Heuristics trade optimality for speed, providing good, though not necessarily perfect, solutions in a reasonable timeframe. These algorithms employ simplified rules or strategies to quickly explore the solution space, making them suitable for real-time applications and large datasets. The acceptable level of accuracy loss is dependent on the specific application and can be tuned by adjusting the heuristic’s parameters. Common heuristic approaches include greedy algorithms, local search, and genetic algorithms, each offering different trade-offs between solution quality and computational cost.

PrimalDualDynamicPricing algorithms represent a class of optimization techniques used to solve dynamic resource allocation and pricing problems, especially those involving capacity constraints. These algorithms function by maintaining a dual decomposition of the problem, iteratively updating prices (primal variables) and allocating resources based on shadow prices (dual variables). This iterative process continues until a Nash equilibrium is achieved, ensuring that resources are allocated efficiently given the constraints and that no participant can improve their outcome by unilaterally changing their strategy. The method is particularly effective in environments with complex constraints, such as limited inventory or production capacity, and scales well to large-scale problems, making it suitable for applications like revenue management, supply chain optimization, and network resource allocation.

The Multinomial Logit Model (MNLModel) is a statistical method used to predict the probability of a customer selecting a specific item from a choice set. It assumes that the utility a customer derives from each item is composed of a deterministic component, representing the inherent value of the item, and a random error term. This model calculates choice probabilities based on the ratio of utilities, expressed as $P(i) = \frac{e^{U_i}}{\sum_{j=1}^{J} e^{U_j}}$, where $U_i$ is the utility of item $i$ and $J$ is the total number of items in the choice set. In assortment optimization, the MNLModel is used to estimate the impact of different product assortments on predicted demand, enabling algorithms to identify the assortment that maximizes expected revenue or profit by predicting which items customers are most likely to purchase.

Evolving Strategies: Reinforcement Learning and Adaptive Pricing

ContextualBandit algorithms address the exploration-exploitation dilemma in dynamic pricing by treating price selection as a multi-armed bandit problem with state-dependent reward distributions. Each price point is an ‘arm’, and the ‘context’ is defined by factors such as customer characteristics, time of day, and inventory levels. The algorithm learns a policy that selects prices to maximize cumulative revenue, balancing the need to ‘exploit’ current best estimates of optimal prices with the need to ‘explore’ alternative prices to refine those estimates. Unlike traditional A/B testing, ContextualBandits dynamically adjust price selection based on observed rewards, converging more efficiently to optimal pricing strategies, particularly in environments with high dimensionality and non-stationary demand.

Regularized Maximum Likelihood Pricing (RMLP) utilizes statistical learning techniques to estimate price sensitivity from high-dimensional datasets, such as those incorporating numerous product features, customer demographics, and historical sales data. The core principle involves maximizing the likelihood of observed purchase behavior while simultaneously applying regularization terms – typically $L_1$ or $L_2$ penalties – to the model parameters. These penalties constrain model complexity, effectively preventing overfitting to the training data and improving generalization performance on unseen data. By controlling model complexity, RMLP enhances the robustness of the pricing model, leading to more stable and reliable price predictions, particularly in scenarios with limited data or high levels of noise. This approach is beneficial for accurately estimating demand curves and identifying optimal pricing strategies.

Incentive compatibility in dynamic pricing mechanisms ensures that consumers truthfully reveal their preferences to the system. This is achieved by designing pricing structures where reporting one’s true willingness to pay maximizes the consumer’s expected utility, regardless of the actions of other consumers. Specifically, the mechanism must satisfy the condition that truthful reporting constitutes a dominant strategy for each consumer; any attempt to misreport preferences should not yield a better outcome for the consumer. This principle is crucial for building trust and fairness, as it prevents manipulation of the pricing system and encourages honest participation, ultimately leading to more efficient price discovery and allocation of goods or services.

Projected Stochastic Gradient Descent (PSGD) is an optimization algorithm used to refine pricing strategies, especially for perishable goods where demand is time-sensitive and inventory diminishes. PSGD updates pricing parameters iteratively based on randomly sampled data points, reducing computational cost compared to batch gradient descent. The “projected” component ensures that updated parameters remain within feasible bounds, preventing prices from becoming negative or exceeding maximum allowable values. This is crucial for perishable items, as outdated prices resulting from slow optimization can lead to unsold inventory and financial loss. PSGD’s stochastic nature allows rapid adaptation to changing demand patterns, while projection maintains practical constraints, yielding improved profitability and reduced waste compared to static pricing models.

The Future Unveiled: Generative AI and DeepRule Frameworks

Generative AI is fundamentally reshaping pricing and assortment optimization by moving beyond traditional, constrained methods. Instead of testing a limited set of pre-defined strategies, these systems can autonomously explore an immense landscape of possibilities, identifying solutions that might remain undiscovered through conventional approaches. This expansive search capability stems from the AI’s ability to learn the intricate relationships between pricing, product assortment, and customer behavior. The result isn’t simply incremental improvement, but the potential for genuinely novel strategies – combinations of price points and product mixes that maximize revenue and customer satisfaction. By synthesizing data and iteratively refining its approach, generative AI delivers dynamic pricing and assortment plans tailored to the unique characteristics of each market and customer segment, offering a significant advantage in increasingly competitive retail environments.

The synthesis of Large Language Models and Monte Carlo Tree Search represents a significant advancement in automated pricing strategy development. This approach allows for the extraction of complex pricing rules directly from data, moving beyond simple correlations to identify nuanced relationships between product attributes, customer behavior, and optimal price points. Unlike traditional methods that often yield opaque ‘black box’ solutions, this combination prioritizes interpretability; the resulting rules are presented in a human-readable format, enabling stakeholders to understand why a particular price is recommended. The Monte Carlo Tree Search acts as a planning algorithm, guiding the Language Model’s exploration of possible rule combinations and evaluating their potential impact on key performance indicators. This process efficiently navigates the vast space of potential pricing strategies, converging on solutions that are not only effective but also transparent and actionable, offering a powerful tool for dynamic pricing in complex retail environments.

Symbolic regression, when paired with the insights of large language models, offers a powerful approach to deciphering the mathematical underpinnings of customer choices. Rather than simply predicting behavior, this technique actively seeks to define the relationships – expressed as equations – that govern purchasing decisions. For example, an LLM might identify key variables like price, seasonality, and competitor offerings, then guide the symbolic regression process to formulate a model such as $Demand = a – b \cdot Price + c \cdot Seasonality$. This allows for a more nuanced understanding of how these factors interact, revealing if demand exhibits linear, exponential, or more complex responses. The resulting equations aren’t merely descriptive; they offer interpretable, actionable insights into customer behavior, potentially uncovering previously unknown sensitivities and enabling retailers to refine pricing and assortment strategies with greater precision.

The DeepRule framework represents a significant advancement in dynamic pricing and assortment strategies by seamlessly integrating knowledge fusion, constrained optimization, and interpretable strategy generation. This holistic approach moves beyond traditional methods, demonstrably accelerating the convergence of pricing models and substantially reducing the Mean Absolute Error (MAE) when benchmarked against both evolutionary algorithms and other Large Language Model-based generative frameworks – a performance difference clearly illustrated in Figure 7. Crucially, the framework doesn’t simply improve predictive accuracy; it also enhances decision-making capabilities within complex retail environments by optimizing performance and reducing model complexity through structural optimizations that refine fitting precision. This allows for the derivation of pricing rules that are not only effective but also readily understandable, providing valuable insights into customer behavior and facilitating more informed business strategies.

After 50 iterations, rule search methods demonstrate varying performance in adversarial evaluation.
After 50 iterations, rule search methods demonstrate varying performance in adversarial evaluation.

The pursuit within DeepRule exemplifies a fundamental tenet of understanding any system: deconstruction to reveal its underlying principles. It mirrors the sentiment expressed by Claude Shannon: “The most important thing is to get the information from point A to point B.” This framework doesn’t merely accept established models of assortment and pricing; it actively probes their limitations by translating complex economic realities into quantifiable, predictive structures. By integrating Large Language Models with symbolic regression, DeepRule effectively dissects the ‘message’ of market data – the intricate interplay of consumer behavior and product attributes – and reconstructs it into actionable strategies. The constrained optimization component then ensures this ‘transmission’ is efficient, delivering optimal decisions despite real-world complexities. It’s a process of intellectual dismantling and rebuilding, guided by the quest for clarity within apparent chaos.

Beyond the Rulebook

The framework presented doesn’t simply find rules; it generates them. This is a crucial distinction, and one that invites scrutiny. What happens when the generated rules defy established economic intuition? Are these anomalies errors to be corrected, or signals of previously unobserved market dynamics? The system’s reliance on predictive modeling begs the question: is it truly optimizing for profit, or merely becoming exceptionally good at predicting existing consumer behavior? A truly robust system would actively shape demand, not just react to it-a shift that demands exploration beyond the current reactive paradigm.

The integration of symbolic regression with large language models is a promising, if precarious, dance. The LLM’s inherent ambiguity, while allowing for creative rule generation, introduces a vulnerability to spurious correlations. Future work must rigorously address the explainability of these generated rules, moving beyond mere predictive accuracy to demonstrable causal relationships. Can the framework be adapted to incorporate counterfactual reasoning, probing the ‘what ifs’ that lie beyond the observed data?

Ultimately, DeepRule represents a step towards automating not just decision making, but the very definition of optimal strategy. The next logical, and perhaps unsettling, evolution lies in allowing the system to challenge the constraints themselves. What happens when the framework begins to renegotiate the fundamental assumptions of assortment and pricing – the very rules by which retail operates? That, it seems, is where the interesting bugs will reside.

Original article: https://arxiv.org/pdf/2512.03607.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/

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2025-12-04 17:03