Systems and methods for optimal bidding in a business to business environment
The present invention relates to systems and methods for optimizing bidding in a business-to-business environment. Initially the observed outcomes for n deals are received, and the belief parameters for these n deals are calculated. The Bayes-greedy price is then calculated and presented to a buyer. The buyer's response is collected and an optimal variance parameter based on the buyer's response is generated. The belief parameters for these n+1 deals are also updated. This process may be repeated for additional deals.
1. A method for reducing computations of non-normal data with a processor, comprising:
receiving, at a processor, features of n events;
receiving, at the processor, observed outcomes of the n events;
calculating, via the processor, a normal distribution of the observed outcomes based on the features; and
when a new event occurs:
calculating a posterior distribution representing regression coefficients of the observed outcomes with the new event, the posterior distribution being a non-normal distribution;
replacing, within memory associated with the processor, the posterior distribution with a normal approximated distribution of the posterior distribution;
calculating a projected outcome of the new event using the normal approximated distribution with the formula: p k−1 =p k −α k ∇ p k R(p k ; x, β); and
outputting the projected outcome to a display.
2. The method of claim 1 , further comprising:
adding the projected outcome to the observed outcomes, resulting in updated projected outcomes; and
recursively updating the normal distribution of the observed outcomes based on the updated projected outcomes.
3. The method of claim 1 , further comprising:
calculating, based at least in part on the projected outcome, an optimal variance parameter.
4. The method of claim 3 , wherein the optimal variance parameter is calculated using the equation: v k+1 =v k −α k {circumflex over (∇)} v k KL (Q∥P).
5. The method of claim 1 , wherein then events comprise previous transactions, and the new event is a new transaction.
6. The method of claim 1 , wherein the formula for calculating the projected outcome is the Bayes-greedy formula.
7. The method of claim 1 , wherein the normal approximated distribution is generated by optimizing a divergence between the posterior distribution and an initial approximation of the posterior distribution, wherein the optimizing uses gradient based stochastic approximation.
8. A system comprising:
a processor; and
a non-transitory computer-readable storage medium having instructions stored which, when executed by the processor, cause the processor to perform operations comprising:
receiving features of n events;
receiving observed outcomes of the n events;
calculating a normal distribution of the observed outcomes based on the features; and
when a new event occurs:
calculating a posterior distribution representing regression coefficients of the observed outcomes with the new event, the posterior distribution being a non-normal distribution;
replacing, within the non-transitory computer-readable storage medium, the posterior distribution with a normal approximated distribution of the posterior distribution;
calculating a projected outcome of the new event using the normal approximated distribution with the formula: p k−1 =p k −α k ∇ p k R(p k ; x, β); and
outputting the projected outcome to a display.
9. The system of claim 8 , the non-transitory computer-readable storage medium having additional instructions stored which, when executed by the processor, cause the processor to perform operations comprising:
adding the projected outcome to the observed outcomes, resulting in updated projected outcomes; and
recursively updating the normal distribution of the observed outcomes based on the updated projected outcomes.
10. The system of claim 8 , the non-transitory computer-readable storage medium having additional instructions stored which, when executed by the processor, cause the processor to perform operations comprising:
calculating, based at least in part on the projected outcome, an optimal variance parameter.
11. The system of claim 10 , wherein the optimal variance parameter is calculated using the equation: v k+1 =v k −α k {circumflex over (∇)} v k KL (Q∥P).
12. The system of claim 8 , wherein the n events comprise previous transactions, and the new event is a new transaction.
13. The system of claim 8 , wherein the formula for calculating the projected outcome is the Bayes-greedy formula.
14. The system of claim 8 , wherein the normal approximated distribution is generated by optimizing a divergence between the posterior distribution and an initial approximation of the posterior distribution, wherein the optimizing uses gradient based stochastic approximation.
15. A non-transitory computer-readable storage medium having instructions stored which, when executed by a processor, cause the processor to perform operations comprising:
receiving features of n events;
receiving observed outcomes of the n events;
calculating a normal distribution of the observed outcomes based on the features; and
when a new event occurs:
calculating a posterior distribution representing regression coefficients of the observed outcomes with the new event, the posterior distribution being a non-normal distribution;
replacing, within the non-transitory computer-readable storage medium, the posterior distribution with a normal approximated distribution of the posterior distribution;
calculating a projected outcome of the new event using the normal approximated distribution with the formula: p k−1 =p k −α k ∇ p k R(p k ; x, β); and
outputting the projected outcome to a display.
16. The non-transitory computer-readable storage medium of claim 15 , having additional instructions stored which, when executed by the processor, cause the processor to perform operations comprising:
adding the projected outcome to the observed outcomes, resulting in updated projected outcomes; and
recursively updating the normal distribution of the observed outcomes based on the updated projected outcomes.
17. The non-transitory computer-readable storage medium of claim 15 , having additional instructions stored which, when executed by the processor, cause the processor to perform operations comprising:
calculating, based at least in part on the projected outcome, an optimal variance parameter.
18. The non-transitory computer-readable storage medium of claim 17 , wherein the optimal variance parameter is calculated using the equation: v k+1 =v k −α k {circumflex over (∇)} v k KL (Q∥P).
19. The non-transitory computer-readable storage medium of claim 15 , wherein then events comprise previous transactions, and the new event is a new transaction.
20. The non-transitory computer-readable storage medium of claim 15 , wherein the formula for calculating the projected outcome is the Bayes-greedy formula.