A Construction of Regret

There are two forms of regret: regret due to a shift of values, and regret due to a change of information. Regret only exists post-hoc, i.e. you can only regret an event which has passed, something you have already experienced.

Let us say at every juncture, you have a set of mutually exclusive actions you may take¹. Further, let us say that you have some black box which outputs an ordered set of actions, or minimally, a single best action. This condition is essentially rationality—rational agents picks the best action—where “best” is subjective, i.e., under the agent’s own, arbitrary, ordering—at every point. We can simplify a little and consider this as feeding information ( ) and a set of actions ( ) into a decision making process ( ) which yields a single action , in short: .

Values

Values naturally change over time—it is hard to care about the economy when you are four, and it is hard to care about your favorite toy truck when you’re forty. Regret here stems from a post-hoc analysis of past actions where, even with the same information, you would choose a different action (or set of actions) since your priorities have shifted. This regret typically only happens when this action has lasting effects.

With our syntax, this is equivalent to only perturbing to which differs in output at at least one juncture.

An example of this kind of regret is regretting how you treated someone as a child, because as an adult with a hopefully more complex and forgiving nature, you understand that your actions were not acceptable, or at least not optimal. You may have extra information insofar as you have more experience and such, but you have no further information at the juncture—you don’t know anything more about the other person. The new information is completely disjoint from that past decision, but has changed your values in a manner which causes an action reorder.

Information

Decisions may become suboptimal once presented with new information². Here, your values may be the same, but you may learn something which re-orders your action ranking—say, you learn that someone really respected your honest, critical opinion but you held your tongue in the past for fear of hurting their feelings. Both of you may express regret about that moment—them that you didn’t say what you truly felt, and perhaps they further regret that they didn’t communicate their stance to you; you would regret not giving your harsher opinion which, we are assuming a priori, would’ve been better than the softer opinion you gave.

With our syntax, this is equivalent to perturbing or as you could gain more information about the juncture, or learn of more potential actions.

This type of regret can sometimes be reduced by open communication, such as in scenarios painted above, but sometimes cannot. Consider gaming³, specifically, say, roulette. Once you learn what number came up, and when it inevitably isn’t yours, your disappointment can be construed as regret—regret that you didn’t pick the winning number. Same for lottos or whathaveyou. This seems a bit unnatural though, so I’d only refer to this type of regret as “aleatoric regret” (as opposed to plain “regret”.)

PS: Note that these examples are random ones I contrived and have no direct link to my experiences.