In Risk of Rain 2, a character’s DPS can be decomposed into the product of several factors, such as base damage, attack speed, and critical strike chance. As a result, linearly stacking items that increase attack speed, critical chance, and similar stats can produce exponential DPS growth. Similarly, survivability can be decomposed into total health multiplied by armor. Because item resources are limited, marginal returns are huge, and the costs of improving different stats are inconsistent, it is worth computing the optimal build in advance under an item-count constraint so that DPS and effective health are maximized. This matters most for the Engineer, because turrets deal damage in a pure stationary-output style.

This article first proves the convergence of the k-means algorithm in a relatively concise and clear way compared with many existing materials online. The second half discusses two variants produced by combining k-means with ideas from GMM and RPCL. This article is not intended as introductory reading for someone encountering k-means for the first time.

This article trains an agent in Python to move from the start to the goal without falling off the cliff. It implements and compares the Sarsa and Q-learning algorithms in reinforcement learning, and discusses the factors that shape the final solution.

Logistic regression is a classification algorithm widely used in industry. Its structure is simple, with the following main advantages and disadvantages:

pros

1. Training and inference are both fast
2. Easy to implement
3. Low memory usage
4. Good interpretability

cons

1. Because it cannot fit nonlinear relationships, it places higher demands on feature engineering.
2. It is relatively sensitive to multicollinearity