There are cases in which the Halacha permits a Jew to benefit from Melacha done by a non-Jew for his benefit. If the Jew already had sufficient light to read, and the non-Jew merely turned on additional lights to supplement the existing light, there is no problem, and he may continue to read.
The Halacha also discusses a case in which the Jew already had light, and the non-Jew entered and inadvertently turned off the lights; upon realizing his mistake, he immediately turned them back on. In such a case, the Jew may benefit from the light, even though the lights were clearly turned on for his benefit. This leniency is based on the principle that whenever the Melacha done by the non-Jew is done to correct an accidental mistake, and he is merely correcting the situation back to the previous state, it is permitted to benefit.
This is analogous to the Halacha of a non-Jew who was adjusting the wicks of a Jew’s candle in order to enhance the flame, but instead, he extinguished the candle. The Jew is permitted to benefit from the candle when the non-Jew rekindles it. Similarly, A Jew may benefit in a case in which a non-Jew accidentally unplugs a hot-plate while cleaning and immediately re-connects it.
A Jew may benefit from a light turned on by a non-Jew if he already had sufficient light for his purposes.
A Jew may benefit from a Melacha done by a non-Jew for his benefit, if the intent is to correct an accidental mistake.