"while regretting" is correct and usable in written English.
You can use it to describe an emotion that someone feels while performing an action. Example: She approached him while regretting that she had to tell him the news.
I dimly recall "Fuerzabruta," the pseudo-sequel to the long-running "De La Guarda," as an hour and change of high-level anxiety in which I was forced to dodge the performers flitting through the crowd, all the while regretting that I'd worn suede shoes.
Many praised Kok's integrity, while regretting that his successful political career in The Netherlands had ended on this sombre note.
But that would be the charm of it I reflected, while regretting that I did not have time to make the walk.
Hollywood actor Hugo Weaving recently praised Australia's behind-the-camera talent while regretting it did not lead to more homegrown box office successes.
While regretting the "abhorrent violations of human dignity" that took place in Kenya, Hague did not admit government liability and indicated it would defend future claims for compensation.
"I ask myself, 'What is the real strategic interest of the U.S. in Afghanistan?' " he said, while regretting cuts in Washington's $350 million aid package to Colombia, which "is peanuts compared to what you're spending" elsewhere.
After that potentially painful segment ("You may for a while regret your experimental courage," the website notes) you will feel a beating pulse inside your abdomen, creating a feeling of "restlessness, amazement, and elation".
For a while she regretted having escaped from her trafficker, and thought returning to her existence as a sex slave might be preferable.
Macmillan CEO Annette Thomas, while "deeply regretting" the case, states that the company "will not tolerate any form of potentially unlawful behaviour, as our approach to the SFO has demonstrated".
Memory holds you down while regret and sorrow kick hell out of you.
Common choices for loss functions are self information, 0/1 loss and mean square error, while regret and redundancy often adopt KL-divergence.
