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Event-triggered interactive gradient descent for real-time multi-objective optimization

This paper proposes an event-triggered interactive gradient descent method for solving multi-objective optimization problems. We consider scenarios where a human decision maker works with a robot in a supervisory manner in order to find the best Pareto solution to an optimization problem. The human has a time-invariant function that represents the value she gives to the different outcomes. However, this function is implicit, meaning that the human does not know it in closed form, but can respond to queries about it. We provide event-triggered designs that allow the robot to efficiently query the human about her preferences at discrete instants of time. For both the cases when the human can answer instantaneously and with some bounded delay, we establish the existence of a minimum interexecution time and the global asymptotic convergence of the resulting executions to the solution of the multi-objective optimization problem.