Exploration spends a defined reward budget to learn about eligible alternatives

In a simple epsilon-greedy policy, choose a specified greedy action most of the time and choose uniformly from the eligible set during exploration. The greedy action also receives its share of the uniform branch. Ties need a documented rule. If availability filters change, the probability denominator changes for that context; logging one global epsilon value is therefore insufficient to reconstruct every action's propensity. A slate policy has additional combinatorial and interaction choices, so an item-level epsilon rule should not be presented as a complete slate randomization contract.

Cold start can use item content, context, population priors, or carefully designed initial exposure while uncertainty remains high. Absence of clicks on an unshown item is not a known negative. Priors can improve early estimates but can also transfer misleading population averages to a new cohort. Preserve eligibility and the declared outcome requirements during exploration, then evaluate how quickly useful information arrives and how costly the exploration was. Exploration over an allowed set gives no support for an action that the system always filters out.

A common bandit quantity compares expected reward with an oracle that knows the best eligible action's mean for the same context. Summing those mean gaps gives expected pseudo-regret under a stated environment. This is not the same as comparing realized clicks with a lucky sequence of random rewards. A stationary finite-action example can illustrate the arithmetic, while real contexts and preferences can drift. Claims about sublinear regret need the particular algorithm and assumptions that prove them, not the mere presence of random exploration.

Choosing clicks as reward defines a click-maximization problem. It does not establish that higher click reward improves satisfaction, learning, or long-term user benefit. Delayed rewards, repeated recommendations, inventory effects, and interactions between users or items can violate a simple contextual-bandit abstraction. Evaluate the actual policy horizon and relevant outcomes instead of treating a short-term regret calculation as a universal product guarantee. Off-policy comparison also inherits support and logging assumptions; exploration can help collect supported evidence without eliminating every causal or measurement problem.

Track exposure probability, unique explored items, reward delay, uncertainty, and quality by cold-start cohort. Log the actual chosen probability and policy version so future evaluation can reconstruct the action mechanism. Revisit priors and exploration allocation as feedback arrives, but record changes rather than pooling them as one fixed policy. Compare short-run cost with later learning benefit under a designed experiment. A popular-item average can hide poor experience for new users or creators, while a high diversity count alone says nothing about whether explored recommendations were useful.

The probability lab can display a fixed rare-action count. Reset, set both p=0.04 and n=25, predict mean one and variance 0.96, then Play or Step. Reset and set both p=0.04 and n=30 for mean 1.2 and variance 1.152. The bars are exact binomial masses under independent fixed-probability choices; playback highlights outcomes rather than generating samples. The trial slider stops at thirty. It has no contexts, adaptive estimates, rewards, regret, or slate constraints, so it cannot establish a learning guarantee for the exploration policy.