  Multi-arm bandits are gaining popularity as they enable real-world sequential
decision-making across application areas, including clinical trials,
recommender systems, and online decision-making. Consequently, there is an
increased desire to use the available adaptively collected datasets to
distinguish whether one arm was more effective than the other, e.g., which
product or treatment was more effective. Unfortunately, existing tools fail to
provide valid inference when data is collected adaptively or require many
untestable and technical assumptions, e.g., stationarity, iid rewards, bounded
random variables, etc. Our paper introduces the design-based approach to
inference for multi-arm bandits, where we condition the full set of potential
outcomes and perform inference on the obtained sample. Our paper constructs
valid confidence intervals for both the reward mean of any arm and the mean
reward difference between any arms in an assumption-light manner, allowing the
rewards to be arbitrarily distributed, non-iid, and from non-stationary
distributions. In addition to confidence intervals, we also provide valid
design-based confidence sequences, sequences of confidence intervals that have
uniform type-1 error guarantees over time. Confidence sequences allow the agent
to perform a hypothesis test as the data arrives sequentially and stop the
experiment as soon as the agent is satisfied with the inference, e.g., the mean
reward of an arm is statistically significantly higher than a desired
threshold.
