Greedy vs dynamic programming: greedy makes locally optimal choices, DP considers all subproblems

Overlapping subproblems

Dynamic programming solves overlapping subproblems by storing results of subproblems to avoid redundant calculations

Greedy vs beam search decoding: greedy picks best token, beam maintains k candidates

Greedy picks best token, beam maintains k candidates

P

P vs NP asks if every problem whose solution is quickly verifiable can also be quickly solved

approximation algorithms guarantee: solution within factor α of optimal

Approximation algorithms guarantee a solution within a factor α of the optimal solution

DPO simplifies: removes the explicit reward model, trains directly on preferences

DPO simplifies: removes explicit reward model, trains directly on preferences

second-order methods (Newton's) converge faster but are expensive: O(n³) per step

Second-order methods converge faster due to quadratic convergence but are expensive due to O(n³) per iteration