Which adjective best describes someone who shows no restraint in their actions, particularly in indulgent behaviors?

The term that best describes someone who shows no restraint in their actions, particularly in indulgent behaviors, is "licentious." This adjective specifically refers to a lack of moral restraint, especially in sexual conduct and indulgent behaviors. It indicates a disregard for rules or conventions, often leading to excessive and uninhibited actions.

In contrast, the other terms do not convey this idea of unchecked behavior. "Indefatigable" describes someone who is tireless and persistent, often in a positive light—indicating resilience rather than indulgence. "Inimitable" refers to something so unique or excellent that it cannot be replicated, which does not relate to restraint or indulgent behavior. "Inveterate" describes someone deeply entrenched in a habitual behavior, often with a negative connotation, but it does not specifically address a lack of restraint related to indulgence; it can encompass positive or neutral habits as well. Thus, "licentious" is the most fitting descriptor in this context.