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You can refund gas cost to the transaction sender. You can do this with a modifier. Here is an example:

pragma solidity^0.4.11;

contract SomeContract {
    
    event SomeEvent(address sender);
    
    // Need to allow depositing ehter to the contract
    function() public payable {
    }

    modifier refundGasCost()
    {
        uint gasStart = msg.gas;

        _;
        
        uint gasEnd = msg.gas;
        uint usedGas = gasEnd - gasStart;
        // Add intrinsic gas and transfer gas
        usedGas = usedGas + 21000 + 9700;
        // Possibly need to check gasprice here to limit possibility for abuse.
        uint gasCost = usedGas * tx.gasprice;
        // Refund gas cost
        msg.sender.transfer(gasCost);
    }

    function doSomething() external refundGasCost {
        SomeEvent(msg.sender);  
    }
}

Refunding in this way implies some overhead: at least 9700 gas has to be payed extra for the transfer function call inside refundGasCost modifier. Also gas for computations and variables access in refundGasCost should be added to usedGas.

Also the above code is potentially vulnerable to reentrancy and other attacks. I provided it only as an example and didn't test it thoroughly.