CS计算机代考程序代写 AI Web Building Data

Web Building Data
Probability of being caught with web size w
Probability of catching prey with web size w
Energy cost of building web of size w with current weight s Basal metabolic expenditure
Energy value of prey
Weight, st Actions
Websize,w∈W ={4,8,12} Value Function
Vt(st) is the maximum probability of reaching 80 mg by the end of Day 10 starting Day t with weight st.
􏰀1, ifs10≥80 V10(s10) = 0, if s10 < 80 Vt(st)=1ifst ≥80  β w × 0  Vt(st) = max +(1 − βw)λwVt+1(st − αm + b − αw(sw)) w∈W  +(1 − βw)(1 − λw)Vt+1(st − αm − αw(sw))  We want to explore the optimal action associated with V0(s0) for varying val- ues of s0. 1 βw λw αw (s) αm b Stages Days, t State Democracy Data dj Desirable representatives for city j Stages Cities, j ∈ {1, 2, 3} State Number of unallocated representatives, sj Actions Number to allocate to city j, aj Value Function Vj (sj ) is minimum of the maximum discrepancy between the desired and ac- tualnumberofrepresentativesforcitiesj,...,3withsj available. We want V1(3). V3(s3) = |d3 − s3| Vj(sj)= min {max(|dj −aj|,Vj+1(sj −aj))} 0≤aj ≤sj 2 Altitude Data hij maximum altitude of road from i to j Stages Cities, i ∈ {A, B, . . . , J} State None Actions Next city to visit, ai Value Function Vi is minimum maximum altitude of driving from i to J. VJ =0 WewantVA. Vi = min {max(hij,Vj)} j∈D(i) 3 Betting Data p Probability of winning Stages Games, j ∈ {1, 2, 3} State How much money she has, $sj Actions How much to bet on game j, bj Value Function Vj(sj) is maximum probability of having at least $5 after three games if we start game j with $sj . Vj(sj) = We want V1(2). 􏰀 1, if s4 ≥ 5 V4(s4) = 0, if s4 < 5 max {pVj+1(sj + bj) + (1 − p)Vj+1(sj − bj)} 0≤bj ≤sj 4 Advertising Data psa probability of high sales if sales were s and we take action a rs revenue ($) if sales are s c cost ($) of changing production d cost ($) of advertising Stages Weeks, t ∈ {1, 2, 3, 4} State Sales level in previous week, st ∈ {H, L} Actions Advertise,at ∈{Y,N} Value Function Vt(st) is maximum expected profit for weeks t, . . . , 4 if we start week t with st sales in the previous week. V5(s5) = 0 􏰀 pHY(rH −d+Vt+1(H))+(1−pHY)(rL −d−c+Vt+1(L)) [at =Y] Vt(H)=max pHN(rH +Vt+1(H))+(1−pHN)(rL −c+Vt+1(L)) [at =N] 􏰀 pLY(rH −d−c+Vt+1(H))+(1−pLY)(rL −d+Vt+1(L)) [at =Y] Vt(L)=max pLN(rH −c+Vt+1(H))+(1−pLN)(rL +Vt+1(L)) [at =N] WewantV1(s1)fors1 ∈{H,L}. 5