This post explores the inherent explainability of linear programs (LPs). It argues that the optimal solution of an LP and its sensitivity to changes in constraints or objective function are readily understandable through the dual program. The dual provides shadow prices, representing the marginal value of resources, and reduced costs, indicating the improvement needed for a variable to become part of the optimal solution. These values offer direct insights into the LP's behavior. Furthermore, the post highlights the connection between the simplex algorithm and sensitivity analysis, explaining how pivoting reveals the impact of constraint adjustments on the optimal solution. Therefore, LPs are inherently explainable due to the rich information provided by duality and the simplex method's step-by-step process.
The blog post explores using linear programming to optimize League of Legends character builds. It frames the problem of selecting items to maximize specific stats (like attack damage or ability power) as a linear program, where item choices are variables and stat targets are constraints. The author details the process of gathering item data, formulating the linear program, and solving it using Python libraries. They showcase examples demonstrating how this approach can find optimal builds based on desired stats, including handling gold constraints and complex item interactions like Ornn upgrades. While acknowledging limitations like the exclusion of active item effects and dynamic gameplay factors, the author suggests the technique offers a powerful starting point for theorycrafting and understanding item efficiency in League of Legends.
HN users generally praised the approach of using linear programming for League of Legends item optimization, finding it clever and interesting. Some expressed skepticism about its practical application, citing the dynamic nature of the game and the difficulty of accurately modeling all variables, like player skill and enemy team composition. A few pointed out existing tools that already offer similar functionality, like Championify and Probuilds, though the author clarified their focus on exploring the optimization technique itself rather than creating a fully realized tool. The most compelling comments revolved around the limitations of translating theoretical optimization into in-game success, highlighting the gap between mathematical models and the complex reality of gameplay. Discussion also touched upon the potential for incorporating more dynamic factors into the model, like build paths and counter-building, and the ethical considerations of using such tools.
Summary of Comments ( 14 )
https://news.ycombinator.com/item?id=42976244
Hacker News users discussed the practicality and limitations of explainable linear programs (XLPs) as presented in the linked article. Several commenters questioned the real-world applicability of XLPs, pointing out that the constraints requiring explanations to be short and easily understandable might severely restrict the solution space and potentially lead to suboptimal or unrealistic solutions. Others debated the definition and usefulness of "explainability" itself, with some suggesting that forcing simple explanations might obscure the true complexity of a problem. The value of XLPs in specific domains like regulation and policy was also considered, with commenters noting the potential for biased or manipulated explanations. Overall, there was a degree of skepticism about the broad applicability of XLPs while acknowledging the potential value in niche applications where transparent and easily digestible explanations are paramount.
The Hacker News post "Explainable Linear Programs," linking to a blog post by Jeremy Kun, has generated a modest discussion with a few insightful comments. Several commenters engage with the core idea of explainable AI (XAI) applied to linear programming, raising both practical considerations and theoretical points.
One commenter highlights the value of Kun's approach, emphasizing that explaining why a particular solution is optimal can be far more useful than simply presenting the optimal solution itself. They point out that understanding the underlying reasons for optimality can help in decision-making processes, especially when stakeholders need to be convinced or when adapting the model to changing conditions. This commenter sees potential in extending these explainability concepts to more complex optimization problems.
Another commenter questions the practicality of applying XAI to large-scale linear programs. They argue that in real-world scenarios with millions of variables, providing a human-understandable explanation might become incredibly complex and potentially overwhelming. This raises the issue of balancing explainability with scalability in practical applications.
Further discussion centers around the specific techniques Kun uses, with one commenter suggesting connections to duality theory in linear programming. They posit that the explanations generated by Kun's method might be related to the dual variables and the economic interpretations they offer. This suggests a deeper theoretical underpinning to the proposed approach.
A different commenter takes a more critical stance, arguing that the concept of "explainability" itself is often ill-defined. They contend that what constitutes a "good" explanation is subjective and context-dependent. This comment highlights the broader challenges within the XAI field, where standardized metrics and evaluation criteria are still developing.
Finally, one commenter notes the potential benefits of Kun's approach for debugging linear programs. They suggest that by understanding the logic behind the optimal solution, it becomes easier to identify errors or inconsistencies in the model formulation. This practical perspective underscores the utility of XAI beyond just providing explanations for end-users.
While the discussion on Hacker News isn't extensive, it touches upon important facets of XAI in the context of linear programming, from theoretical foundations to practical implications and challenges.