I’m trying to write a custom loss function with some specific logic and having a hard time coming up with a reformulation/approximation of that logic that is differentiable. I would love any help or suggestions that anyone may have on how I might proceed.
The loss function calculates how much money is gained or lost from betting on games. The logic I’ve implemented (but can’t figure out how to reformulate/approximate as differentiable) is: The model can predict three choices [no_bet, bet_on_home, bet_on_away]. Predicting no_bet adds zero to the loss. Incorrectly predicting to bet on home or away adds +1 to the loss. Correctly predicting to bet on home or away subtracts odds - 1 for that team from the loss.
For example, for a model output, target y (where 0 is a home win and 1 is an away win), and list of odds (column 0 is odds on home win and column 1 is odds on away win)
output: tensor([[ 0.2370, 0.2679, 0.3858],
[ 0.0401, 0.5379, -0.1788],
[-0.0537, 0.4639, -0.6986],
[-0.0818, 0.6218, -0.5953],
[ 0.1292, 0.1033, -0.1198],
[-0.2797, -0.4663, -0.4223],
[ 0.4070, 0.8124, -0.3414],
[-0.5048, 1.0760, 0.3167]], device='cuda:0',
grad_fn=<AddmmBackward0>)
y: tensor([1, 0, 1, 0, 0, 0, 0, 1], device='cuda:0')
odds: tensor([[2.3000, 1.6667],
[2.3000, 1.6667],
[1.9091, 1.9091],
[1.1429, 6.0000],
[2.2000, 1.7143],
[1.8333, 2.0000],
[1.0905, 8.0500],
[5.0000, 1.2000]])
The following loss functions (which are NOT differentiable, from the argmax and other logic) are an example of the logic I described above.
def betting_loss(output, y, odds):
# apply softmax
whichbets = torch.argmax(torch.exp(F.log_softmax(output, dim = 1)), dim = 1)
# keep only the games with bets places (not no_bet)
betgames = whichbets != 0
# also convert whichbets to [0,1] scale of y by subtracting 1 (2 - > 1, and 1 -> 0)
whichbets = whichbets[betgames] - 1
y = y[betgames]
odds = odds[betgames]
# games won
wins = whichbets == y
losses_loss = torch.sum(~wins)
wins_loss = torch.sum(odds[wins, y[wins]] - 1)
return losses_loss - wins_loss
The same thing, just in loop form for easier comprehension
def betting_loss_loop(output, y, odds):
# apply softmax
whichbets = torch.argmax(torch.exp(F.log_softmax(output, dim = 1)), dim = 1)
# also convert whichbets to [0,1] scale of y by subtracting 1 (2 - > 1, and 1 -> 0)
whichbets = whichbets - 1
loss = 0
for ii, whichbet in enumerate(whichbets):
if whichbet != -1:
if whichbet != y[ii]:
loss += 1
else:
loss -= odds[ii, y[ii]] - 1
return loss
print(betting_loss(output, y, odds))
print(betting_loss_loop(output, y, odds))
gives
tensor(-0.2000, device='cuda:0')
tensor(-0.2000)
Any help would be greatly appreciated. Thank you