Hardness Assumption

Hardness assumptions in computer science explore the computational difficulty of solving specific problems, often used to establish the security of cryptographic systems or the inherent limitations of learning algorithms. Current research focuses on proving hardness for tasks like learning decision trees, estimating probability distributions (e.g., using score estimation), and feature selection (e.g., analyzing the LASSO algorithm), often leveraging connections to well-established problems in lattice-based cryptography or worst-case complexity theory. These findings have significant implications for algorithm design, establishing fundamental limits on what can be efficiently computed and informing the development of more robust and trustworthy machine learning methods. The results also highlight the importance of considering the balance of power between an algorithm and its input data in assessing computational hardness.