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  reward function for sleeping

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  3D reward function of bedtime and duuration

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  2D reward function of bedtime and duration

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  reward function for meals

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Autonomous Time Management Planner (ATMP)

Updated: January 26, 2020, by June Hu

This task scheduler (a.k.a. time planner) aims to automatically, scientifically schedule various activities for students.

With an input todo-list (an example is shown here), the system calculates the reward function based on real-life experience, for example, fixed-time tasks like lectures and fixed-deadline tasks like assignments generally have higher value in productivity, and fun activities have higher value in enjoyment. The scheduler takes both "$productivity$" and "$enjoyment$" into consideration, with a parameter called "$strictness$" to balance the two. The final reward value of a task would be the linear combination of productivity and enjoyment: $$ reward=strictness*productivity+(1-strictness)*enjoyment, $$ and the total reward value of a schedule is the sum of all the activities in the schedule: $$ reward_{schedule}=\sum{reward_{task}}. $$ The system applies iterative loops to search for an optimization solution to maximize the total reward value, in order to find the optimal schedule.

Define reward functions

Activity types

Activity of different types have different time-dependent curves multiply user-defined $reward$ value to calculate their real rewards. The type list in the system is as follows:

• Sleeping
• Meals
• Fixed-time tasks
• Fixed-deadline tasks
• As-soon-as-possible tasks
• Fun tasks
• Long-term tasks
• Daily-necessity tasks

And we will briefly introduce how the time-dependent reward curve for each type of activity is defined in the following sections.

Sleeping

• Parameters for a sleeping activity: "$bedtime$" and "$duration$" hours
• $bedtime$: typically range from 22:00 to 4:00
• $duration$: typically range from 5 to 12 hours
• $reward$ increases with earlier $bedtime$ and longer $duration$: $$ rwd_{bed} = exp{-(bed_{real}-bed_{min})}, $$ $$ rwd_{dur} = 1-exp{-0.8 * (dur_{real}-dur_{min})} (\text{for } dur_{min} \leqslant dur_{real} \leqslant dur_{max}), $$ $$ rwd = rwd_{bed} * rwd_{dur}. $$

The diagrams of and show the dependent relationships. It makes sense that if I sleep really late (e.g. 4am), even if sleeping for a long period of time cannot undo the harm from the stay up to the body.

Therefore, for me, the parameters are: $dur_{min} = 5, dur_{max} = 12, bed_{min} = 22, bed_{max} = 4$, and here is a diagram of reward to each pair of {$duration$, $bedtime$} in a discrete time step.

Meals

• Parameters: $time$
• suggested time period for three meals: [7, 10], [11, 14], [17, 20]
• It's better to eat within the suggested time period, so time-dependent reward curve:

Fixed-time tasks

• Parameters: $start$, $duration$
• Example: lecture, mandatory activities
• reward doesn't change as long as arrange the activity in the schedule at its arranged time, so the reward curve is a constant over time, and the value is dependent on the $strictness$ according to Equation (1):

Fixed-deadline tasks

As-soon-as-possible tasks

Fun tasks

Long-term tasks

Daily-necessity tasks

Built With

• mathematica
• python