Can a judge revisit his judgment to waive costs imposed on a party on grounds of mercy?

If the judge has decided a case and imposed costs on one party, can he rejudge the matter and waive the costs if approached by the affected party on grounds of compassion? Is there any authority on reexercise of discretion by a judge in a civil or criminal proceeding?

What is a VPN?

VPN is (Virtual Private Network) were first used by companies to enable their employees to securely access internal systems such as email remotely (e.g. from home or while on business trips). Today they are increasingly being used for personal use by individuals to protect their privacy while online in public places (e.g. when using the wi-fi connection in a cafe) or in a country where the internet is censored / blocked (e.g. China, Saudi Arabia…).